TSTP Solution File: LCL085-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL085-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n008.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 08:17:21 EDT 2023
% Result : Unsatisfiable 221.61s 29.08s
% Output : Proof 242.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL085-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 05:21:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 221.61/29.08 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 221.61/29.08
% 221.61/29.08 % SZS status Unsatisfiable
% 221.61/29.08
% 226.97/29.66 % SZS output start Proof
% 226.97/29.66 Take the following subset of the input axioms:
% 226.97/29.66 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(implies(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 226.97/29.66 fof(ic_JLukasiewicz, axiom, ![Z, U, X2, Y2]: is_a_theorem(implies(implies(implies(X2, Y2), Z), implies(implies(Z, X2), implies(U, X2))))).
% 226.97/29.66 fof(prove_ic_5, negated_conjecture, ~is_a_theorem(implies(a, implies(implies(a, b), b)))).
% 226.97/29.66
% 226.97/29.66 Now clausify the problem and encode Horn clauses using encoding 3 of
% 226.97/29.66 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 226.97/29.66 We repeatedly replace C & s=t => u=v by the two clauses:
% 226.97/29.66 fresh(y, y, x1...xn) = u
% 226.97/29.66 C => fresh(s, t, x1...xn) = v
% 226.97/29.66 where fresh is a fresh function symbol and x1..xn are the free
% 226.97/29.66 variables of u and v.
% 226.97/29.66 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 226.97/29.66 input problem has no model of domain size 1).
% 226.97/29.66
% 226.97/29.66 The encoding turns the above axioms into the following unit equations and goals:
% 226.97/29.66
% 226.97/29.66 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 226.97/29.66 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 226.97/29.66 Axiom 3 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 226.97/29.66 Axiom 4 (ic_JLukasiewicz): is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X)))) = true.
% 226.97/29.66
% 226.97/29.66 Lemma 5: fresh2(is_a_theorem(implies(implies(X, Y), Z)), true, implies(implies(Z, X), implies(W, X))) = is_a_theorem(implies(implies(Z, X), implies(W, X))).
% 226.97/29.66 Proof:
% 226.97/29.66 fresh2(is_a_theorem(implies(implies(X, Y), Z)), true, implies(implies(Z, X), implies(W, X)))
% 226.97/29.66 = { by axiom 3 (condensed_detachment) R->L }
% 226.97/29.66 fresh(is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X)))), true, implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X)))
% 226.97/29.66 = { by axiom 4 (ic_JLukasiewicz) }
% 226.97/29.66 fresh(true, true, implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X)))
% 226.97/29.66 = { by axiom 2 (condensed_detachment) }
% 226.97/29.66 is_a_theorem(implies(implies(Z, X), implies(W, X)))
% 226.97/29.66
% 226.97/29.66 Lemma 6: is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W)))) = true.
% 226.97/29.66 Proof:
% 226.97/29.66 is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 226.97/29.66 = { by lemma 5 R->L }
% 226.97/29.66 fresh2(is_a_theorem(implies(implies(implies(Y, W), X), implies(implies(X, Y), implies(Z, Y)))), true, implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 226.97/29.66 = { by axiom 4 (ic_JLukasiewicz) }
% 226.97/29.66 fresh2(true, true, implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 226.97/29.66 = { by axiom 1 (condensed_detachment) }
% 226.97/29.66 true
% 226.97/29.66
% 226.97/29.66 Lemma 7: fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W))), true, implies(V, implies(Y, W))) = is_a_theorem(implies(V, implies(Y, W))).
% 226.97/29.66 Proof:
% 226.97/29.66 fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W))), true, implies(V, implies(Y, W)))
% 226.97/29.66 = { by axiom 3 (condensed_detachment) R->L }
% 226.97/29.66 fresh(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W)))), true, implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W)))
% 226.97/29.66 = { by lemma 6 }
% 226.97/29.66 fresh(true, true, implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W)))
% 226.97/29.66 = { by axiom 2 (condensed_detachment) }
% 226.97/29.66 is_a_theorem(implies(V, implies(Y, W)))
% 226.97/29.66
% 226.97/29.66 Lemma 8: fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), Z)), true, implies(W, Z)) = is_a_theorem(implies(W, Z)).
% 226.97/29.66 Proof:
% 226.97/29.66 fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), Z)), true, implies(W, Z))
% 226.97/29.66 = { by axiom 3 (condensed_detachment) R->L }
% 226.97/29.66 fresh(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), Z), implies(W, Z))), true, implies(implies(implies(X, Y), implies(Y, implies(X, Y))), Z), implies(W, Z))
% 226.97/29.66 = { by lemma 5 R->L }
% 226.97/29.66 fresh(fresh2(is_a_theorem(implies(implies(Z, V), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), Z), implies(W, Z))), true, implies(implies(implies(X, Y), implies(Y, implies(X, Y))), Z), implies(W, Z))
% 226.97/29.66 = { by lemma 7 R->L }
% 226.97/29.66 fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(U, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, implies(implies(Z, V), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), Z), implies(W, Z))), true, implies(implies(implies(X, Y), implies(Y, implies(X, Y))), Z), implies(W, Z))
% 226.97/29.66 = { by lemma 6 }
% 226.97/29.66 fresh(fresh2(fresh2(true, true, implies(implies(Z, V), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), Z), implies(W, Z))), true, implies(implies(implies(X, Y), implies(Y, implies(X, Y))), Z), implies(W, Z))
% 226.97/29.66 = { by axiom 1 (condensed_detachment) }
% 226.97/29.66 fresh(fresh2(true, true, implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), Z), implies(W, Z))), true, implies(implies(implies(X, Y), implies(Y, implies(X, Y))), Z), implies(W, Z))
% 226.97/29.66 = { by axiom 1 (condensed_detachment) }
% 226.97/29.66 fresh(true, true, implies(implies(implies(X, Y), implies(Y, implies(X, Y))), Z), implies(W, Z))
% 226.97/29.66 = { by axiom 2 (condensed_detachment) }
% 226.97/29.66 is_a_theorem(implies(W, Z))
% 226.97/29.66
% 226.97/29.66 Lemma 9: is_a_theorem(implies(implies(X, Y), implies(Z, implies(X, Y)))) = true.
% 226.97/29.66 Proof:
% 226.97/29.66 is_a_theorem(implies(implies(X, Y), implies(Z, implies(X, Y))))
% 226.97/29.66 = { by axiom 2 (condensed_detachment) R->L }
% 226.97/29.66 fresh(true, true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))
% 226.97/29.66 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.66 fresh(fresh2(true, true, implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))
% 226.97/29.66 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.66 fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(S, implies(Y, S)), Y), implies(X, Y)), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(Z, implies(X, Y))))), true, implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))
% 226.97/29.66 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.66 fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(Z, implies(X, Y)), X2), implies(implies(implies(S, implies(Y, S)), Y), implies(X, Y)))), true, implies(implies(implies(implies(implies(S, implies(Y, S)), Y), implies(X, Y)), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(Z, implies(X, Y))))), true, implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))
% 226.97/29.66 = { by axiom 4 (ic_JLukasiewicz) R->L }
% 226.97/29.66 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(Y, S), implies(S, implies(Y, S))), implies(implies(implies(S, implies(Y, S)), Y), implies(X, Y)))), true, implies(implies(implies(Z, implies(X, Y)), X2), implies(implies(implies(S, implies(Y, S)), Y), implies(X, Y)))), true, implies(implies(implies(implies(implies(S, implies(Y, S)), Y), implies(X, Y)), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(Z, implies(X, Y))))), true, implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))
% 226.97/29.66 = { by lemma 8 }
% 226.97/29.66 fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(Z, implies(X, Y)), X2), implies(implies(implies(S, implies(Y, S)), Y), implies(X, Y)))), true, implies(implies(implies(implies(implies(S, implies(Y, S)), Y), implies(X, Y)), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(Z, implies(X, Y))))), true, implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))
% 226.97/29.66 = { by lemma 5 }
% 226.97/29.66 fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(S, implies(Y, S)), Y), implies(X, Y)), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(Z, implies(X, Y))))), true, implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))
% 226.97/29.66 = { by lemma 7 }
% 226.97/29.66 fresh(is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, Y), implies(Z, implies(X, Y))))
% 226.97/29.66 = { by axiom 3 (condensed_detachment) }
% 226.97/29.66 fresh2(is_a_theorem(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W)))), true, implies(implies(X, Y), implies(Z, implies(X, Y))))
% 226.97/29.66 = { by axiom 4 (ic_JLukasiewicz) }
% 226.97/29.66 fresh2(true, true, implies(implies(X, Y), implies(Z, implies(X, Y))))
% 226.97/29.66 = { by axiom 1 (condensed_detachment) }
% 226.97/29.66 true
% 226.97/29.66
% 226.97/29.66 Lemma 10: is_a_theorem(implies(X, implies(implies(Y, Y), implies(Y, Y)))) = true.
% 226.97/29.66 Proof:
% 226.97/29.66 is_a_theorem(implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.66 = { by axiom 2 (condensed_detachment) R->L }
% 226.97/29.66 fresh(true, true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.66 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.66 fresh(fresh2(true, true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.66 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.66 fresh(fresh2(fresh2(true, true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.66 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.67 fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(Y, Y), implies(Y, Y)), Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by lemma 9 R->L }
% 226.97/29.67 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))), true, implies(implies(implies(implies(Y, Y), implies(Y, Y)), Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by lemma 5 }
% 226.97/29.67 fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(Y, Y), implies(Y, Y)), Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by lemma 5 }
% 226.97/29.67 fresh(fresh2(is_a_theorem(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by axiom 3 (condensed_detachment) R->L }
% 226.97/29.67 fresh(fresh(is_a_theorem(implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by lemma 5 R->L }
% 226.97/29.67 fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by axiom 2 (condensed_detachment) R->L }
% 226.97/29.67 fresh(fresh(fresh2(fresh(true, true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.67 fresh(fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.67 fresh(fresh(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(Y, Y), implies(Y, Y)), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.67 fresh(fresh(fresh2(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(Y, Y)), implies(implies(Y, Y), implies(Y, Y)))), true, implies(implies(implies(implies(Y, Y), implies(Y, Y)), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by lemma 9 R->L }
% 226.97/29.67 fresh(fresh(fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(Y, Y), implies(Y, Y)), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(Y, Y)), implies(implies(Y, Y), implies(Y, Y)))), true, implies(implies(implies(implies(Y, Y), implies(Y, Y)), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by lemma 5 }
% 226.97/29.67 fresh(fresh(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(Y, Y)), implies(implies(Y, Y), implies(Y, Y)))), true, implies(implies(implies(implies(Y, Y), implies(Y, Y)), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by lemma 5 }
% 226.97/29.67 fresh(fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(Y, Y), implies(Y, Y)), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by lemma 8 }
% 226.97/29.67 fresh(fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by axiom 3 (condensed_detachment) }
% 226.97/29.67 fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S)))), true, implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.67 = { by axiom 4 (ic_JLukasiewicz) }
% 226.97/29.67 fresh(fresh(fresh2(fresh2(true, true, implies(implies(implies(X, implies(implies(Y, Y), implies(Y, Y))), T), implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.68 = { by axiom 1 (condensed_detachment) }
% 226.97/29.68 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y)))))), true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.68 = { by axiom 1 (condensed_detachment) }
% 226.97/29.68 fresh(fresh(true, true, implies(implies(implies(Y, Y), implies(implies(Y, Y), implies(Y, Y))), implies(X, implies(implies(Y, Y), implies(Y, Y)))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.68 = { by axiom 2 (condensed_detachment) }
% 226.97/29.68 fresh(is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.68 = { by axiom 3 (condensed_detachment) }
% 226.97/29.68 fresh2(is_a_theorem(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z)))), true, implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.68 = { by axiom 4 (ic_JLukasiewicz) }
% 226.97/29.68 fresh2(true, true, implies(X, implies(implies(Y, Y), implies(Y, Y))))
% 226.97/29.68 = { by axiom 1 (condensed_detachment) }
% 226.97/29.68 true
% 226.97/29.68
% 226.97/29.68 Lemma 11: is_a_theorem(implies(X, implies(Y, Y))) = true.
% 226.97/29.68 Proof:
% 226.97/29.68 is_a_theorem(implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 2 (condensed_detachment) R->L }
% 226.97/29.68 fresh(true, true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.68 fresh(fresh2(true, true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.68 fresh(fresh2(fresh2(true, true, implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.68 fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(Y, Y), Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.68 fresh(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(Y, Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 4 (ic_JLukasiewicz) R->L }
% 226.97/29.68 fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(T, S), X2), implies(implies(X2, T), implies(Y2, T)))), true, implies(implies(Y, Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 3 (condensed_detachment) R->L }
% 226.97/29.68 fresh(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(T, S), X2), implies(implies(X2, T), implies(Y2, T))), implies(implies(Y, Y), implies(Y, Y)))), true, implies(implies(implies(T, S), X2), implies(implies(X2, T), implies(Y2, T))), implies(implies(Y, Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by lemma 10 }
% 226.97/29.68 fresh(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(T, S), X2), implies(implies(X2, T), implies(Y2, T))), implies(implies(Y, Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 2 (condensed_detachment) }
% 226.97/29.68 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(Y, Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by lemma 5 }
% 226.97/29.68 fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(Y, Y), Y), implies(Y, Y))), true, implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by lemma 5 }
% 226.97/29.68 fresh(fresh2(is_a_theorem(implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 3 (condensed_detachment) R->L }
% 226.97/29.68 fresh(fresh(is_a_theorem(implies(implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y))))), true, implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by lemma 5 R->L }
% 226.97/29.68 fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(X, implies(Y, Y)), Z2), implies(implies(Y, Y), implies(Y, Y)))), true, implies(implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y))))), true, implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by lemma 10 }
% 226.97/29.68 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y))))), true, implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 1 (condensed_detachment) }
% 226.97/29.68 fresh(fresh(true, true, implies(implies(implies(Y, Y), implies(Y, Y)), implies(X, implies(Y, Y))), implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 2 (condensed_detachment) }
% 226.97/29.68 fresh(is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 3 (condensed_detachment) }
% 226.97/29.68 fresh2(is_a_theorem(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z)))), true, implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 4 (ic_JLukasiewicz) }
% 226.97/29.68 fresh2(true, true, implies(X, implies(Y, Y)))
% 226.97/29.68 = { by axiom 1 (condensed_detachment) }
% 226.97/29.68 true
% 226.97/29.68
% 226.97/29.68 Lemma 12: is_a_theorem(implies(implies(implies(X, X), Y), implies(Z, Y))) = true.
% 226.97/29.68 Proof:
% 226.97/29.68 is_a_theorem(implies(implies(implies(X, X), Y), implies(Z, Y)))
% 226.97/29.68 = { by lemma 5 R->L }
% 226.97/29.68 fresh2(is_a_theorem(implies(implies(Y, W), implies(X, X))), true, implies(implies(implies(X, X), Y), implies(Z, Y)))
% 226.97/29.68 = { by lemma 11 }
% 226.97/29.68 fresh2(true, true, implies(implies(implies(X, X), Y), implies(Z, Y)))
% 226.97/29.68 = { by axiom 1 (condensed_detachment) }
% 226.97/29.68 true
% 226.97/29.68
% 226.97/29.68 Lemma 13: fresh2(is_a_theorem(implies(X, Y)), true, implies(Z, implies(X, Y))) = is_a_theorem(implies(Z, implies(X, Y))).
% 226.97/29.68 Proof:
% 226.97/29.68 fresh2(is_a_theorem(implies(X, Y)), true, implies(Z, implies(X, Y)))
% 226.97/29.68 = { by axiom 3 (condensed_detachment) R->L }
% 226.97/29.68 fresh(is_a_theorem(implies(implies(X, Y), implies(Z, implies(X, Y)))), true, implies(X, Y), implies(Z, implies(X, Y)))
% 226.97/29.68 = { by lemma 9 }
% 226.97/29.68 fresh(true, true, implies(X, Y), implies(Z, implies(X, Y)))
% 226.97/29.68 = { by axiom 2 (condensed_detachment) }
% 226.97/29.68 is_a_theorem(implies(Z, implies(X, Y)))
% 226.97/29.68
% 226.97/29.68 Lemma 14: fresh2(is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))), V)), true, implies(U, V)) = is_a_theorem(implies(U, V)).
% 226.97/29.68 Proof:
% 226.97/29.68 fresh2(is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))), V)), true, implies(U, V))
% 226.97/29.68 = { by axiom 3 (condensed_detachment) R->L }
% 226.97/29.68 fresh(is_a_theorem(implies(implies(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))), V), implies(U, V))), true, implies(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))), V), implies(U, V))
% 226.97/29.68 = { by lemma 5 R->L }
% 226.97/29.68 fresh(fresh2(is_a_theorem(implies(implies(V, T), implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))))), true, implies(implies(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))), V), implies(U, V))), true, implies(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))), V), implies(U, V))
% 226.97/29.68 = { by lemma 13 R->L }
% 226.97/29.68 fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X)))), true, implies(implies(V, T), implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))))), true, implies(implies(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))), V), implies(U, V))), true, implies(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))), V), implies(U, V))
% 226.97/29.68 = { by axiom 4 (ic_JLukasiewicz) }
% 226.97/29.68 fresh(fresh2(fresh2(true, true, implies(implies(V, T), implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))))), true, implies(implies(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))), V), implies(U, V))), true, implies(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))), V), implies(U, V))
% 226.97/29.68 = { by axiom 1 (condensed_detachment) }
% 226.97/29.68 fresh(fresh2(true, true, implies(implies(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))), V), implies(U, V))), true, implies(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))), V), implies(U, V))
% 226.97/29.68 = { by axiom 1 (condensed_detachment) }
% 226.97/29.68 fresh(true, true, implies(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X))), V), implies(U, V))
% 226.97/29.68 = { by axiom 2 (condensed_detachment) }
% 226.97/29.68 is_a_theorem(implies(U, V))
% 226.97/29.68
% 226.97/29.68 Lemma 15: is_a_theorem(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))) = true.
% 226.97/29.68 Proof:
% 226.97/29.68 is_a_theorem(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.68 = { by axiom 2 (condensed_detachment) R->L }
% 226.97/29.68 fresh(true, true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.68 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.68 fresh(fresh2(true, true, implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.68 = { by axiom 4 (ic_JLukasiewicz) R->L }
% 226.97/29.68 fresh(fresh2(is_a_theorem(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S)))), true, implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.68 = { by axiom 3 (condensed_detachment) R->L }
% 226.97/29.68 fresh(fresh(is_a_theorem(implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by lemma 14 R->L }
% 226.97/29.69 fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(X, Y), W2), X), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by lemma 5 R->L }
% 226.97/29.69 fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))), X), implies(implies(implies(X, Y), W2), X))), true, implies(implies(implies(implies(implies(X, Y), W2), X), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by lemma 5 R->L }
% 226.97/29.69 fresh(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(X, Y), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))), X), implies(implies(implies(X, Y), W2), X))), true, implies(implies(implies(implies(implies(X, Y), W2), X), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by axiom 2 (condensed_detachment) R->L }
% 226.97/29.69 fresh(fresh(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(V2, U2), T2), implies(implies(T2, V2), implies(S2, V2))), implies(implies(X, Y), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))), X), implies(implies(implies(X, Y), W2), X))), true, implies(implies(implies(implies(implies(X, Y), W2), X), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.69 fresh(fresh(fresh2(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(V2, U2), T2), implies(implies(T2, V2), implies(S2, V2))), implies(implies(X, Y), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(V2, U2), T2), implies(implies(T2, V2), implies(S2, V2))), implies(implies(X, Y), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))), X), implies(implies(implies(X, Y), W2), X))), true, implies(implies(implies(implies(implies(X, Y), W2), X), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by lemma 9 R->L }
% 226.97/29.69 fresh(fresh(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(implies(V2, U2), T2), implies(implies(T2, V2), implies(S2, V2))), implies(implies(X, Y), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(V2, U2), T2), implies(implies(T2, V2), implies(S2, V2))), implies(implies(X, Y), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))), X), implies(implies(implies(X, Y), W2), X))), true, implies(implies(implies(implies(implies(X, Y), W2), X), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by lemma 7 }
% 226.97/29.69 fresh(fresh(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(V2, U2), T2), implies(implies(T2, V2), implies(S2, V2))), implies(implies(X, Y), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(V2, U2), T2), implies(implies(T2, V2), implies(S2, V2))), implies(implies(X, Y), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))), X), implies(implies(implies(X, Y), W2), X))), true, implies(implies(implies(implies(implies(X, Y), W2), X), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by axiom 3 (condensed_detachment) }
% 226.97/29.69 fresh(fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(V2, U2), T2), implies(implies(T2, V2), implies(S2, V2)))), true, implies(implies(X, Y), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))), X), implies(implies(implies(X, Y), W2), X))), true, implies(implies(implies(implies(implies(X, Y), W2), X), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by axiom 4 (ic_JLukasiewicz) }
% 226.97/29.69 fresh(fresh(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(X, Y), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))), X), implies(implies(implies(X, Y), W2), X))), true, implies(implies(implies(implies(implies(X, Y), W2), X), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by axiom 1 (condensed_detachment) }
% 226.97/29.69 fresh(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))), X), implies(implies(implies(X, Y), W2), X))), true, implies(implies(implies(implies(implies(X, Y), W2), X), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by axiom 1 (condensed_detachment) }
% 226.97/29.69 fresh(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(X, Y), W2), X), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by axiom 1 (condensed_detachment) }
% 226.97/29.69 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))))), true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by axiom 1 (condensed_detachment) }
% 226.97/29.69 fresh(fresh(true, true, implies(implies(implies(S, X2), Y2), implies(implies(Y2, S), implies(Z2, S))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by axiom 2 (condensed_detachment) }
% 226.97/29.69 fresh(is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by axiom 3 (condensed_detachment) }
% 226.97/29.69 fresh2(is_a_theorem(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W)))), true, implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by axiom 4 (ic_JLukasiewicz) }
% 226.97/29.69 fresh2(true, true, implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y))))
% 226.97/29.69 = { by axiom 1 (condensed_detachment) }
% 226.97/29.69 true
% 226.97/29.69
% 226.97/29.69 Lemma 16: fresh2(is_a_theorem(implies(X, implies(X, Y))), true, implies(Z, implies(X, Y))) = is_a_theorem(implies(Z, implies(X, Y))).
% 226.97/29.69 Proof:
% 226.97/29.69 fresh2(is_a_theorem(implies(X, implies(X, Y))), true, implies(Z, implies(X, Y)))
% 226.97/29.69 = { by axiom 3 (condensed_detachment) R->L }
% 226.97/29.69 fresh(is_a_theorem(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), true, implies(X, implies(X, Y)), implies(Z, implies(X, Y)))
% 226.97/29.69 = { by lemma 15 }
% 226.97/29.69 fresh(true, true, implies(X, implies(X, Y)), implies(Z, implies(X, Y)))
% 226.97/29.69 = { by axiom 2 (condensed_detachment) }
% 226.97/29.69 is_a_theorem(implies(Z, implies(X, Y)))
% 226.97/29.69
% 226.97/29.69 Lemma 17: fresh2(is_a_theorem(implies(implies(X, X), Y)), true, Y) = is_a_theorem(Y).
% 226.97/29.69 Proof:
% 226.97/29.69 fresh2(is_a_theorem(implies(implies(X, X), Y)), true, Y)
% 226.97/29.69 = { by axiom 3 (condensed_detachment) R->L }
% 226.97/29.69 fresh(is_a_theorem(implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 226.97/29.69 = { by axiom 2 (condensed_detachment) R->L }
% 226.97/29.69 fresh(fresh(true, true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 226.97/29.69 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.70 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 226.97/29.70 = { by lemma 12 R->L }
% 226.97/29.70 fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(X, X), Y), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 226.97/29.70 = { by lemma 16 }
% 226.97/29.70 fresh(fresh(is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 226.97/29.70 = { by axiom 3 (condensed_detachment) }
% 226.97/29.70 fresh(fresh2(is_a_theorem(implies(implies(implies(Z, W), V), implies(implies(V, Z), implies(U, Z)))), true, implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 226.97/29.70 = { by axiom 4 (ic_JLukasiewicz) }
% 226.97/29.70 fresh(fresh2(true, true, implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 226.97/29.70 = { by axiom 1 (condensed_detachment) }
% 226.97/29.70 fresh(true, true, implies(implies(X, X), Y), Y)
% 226.97/29.70 = { by axiom 2 (condensed_detachment) }
% 226.97/29.70 is_a_theorem(Y)
% 226.97/29.70
% 226.97/29.70 Lemma 18: is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z))) = true.
% 226.97/29.70 Proof:
% 226.97/29.70 is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 2 (condensed_detachment) R->L }
% 226.97/29.70 fresh(true, true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.70 fresh(fresh2(true, true, implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 4 (ic_JLukasiewicz) R->L }
% 226.97/29.70 fresh(fresh2(is_a_theorem(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 3 (condensed_detachment) R->L }
% 226.97/29.70 fresh(fresh(is_a_theorem(implies(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z))))), true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by lemma 5 R->L }
% 226.97/29.70 fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(X, Y)), implies(implies(Z, S), implies(X, Y)))), true, implies(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z))))), true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by lemma 5 R->L }
% 226.97/29.70 fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Y, Z)), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(X, Y)), implies(implies(Z, S), implies(X, Y)))), true, implies(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z))))), true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by lemma 5 R->L }
% 226.97/29.70 fresh(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(Y, Z), Y), implies(X, Y))), true, implies(implies(implies(X, Y), implies(Y, Z)), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(X, Y)), implies(implies(Z, S), implies(X, Y)))), true, implies(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z))))), true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by lemma 5 R->L }
% 226.97/29.70 fresh(fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(Y, Z), implies(Y, Z))), true, implies(implies(implies(Y, Z), Y), implies(X, Y))), true, implies(implies(implies(X, Y), implies(Y, Z)), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(X, Y)), implies(implies(Z, S), implies(X, Y)))), true, implies(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z))))), true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 2 (condensed_detachment) R->L }
% 226.97/29.70 fresh(fresh(fresh2(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(X2, Y2), Z2), implies(implies(Z2, X2), implies(W2, X2))), implies(implies(Y, Z), implies(Y, Z))), true, implies(implies(implies(Y, Z), Y), implies(X, Y))), true, implies(implies(implies(X, Y), implies(Y, Z)), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(X, Y)), implies(implies(Z, S), implies(X, Y)))), true, implies(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z))))), true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by lemma 11 R->L }
% 226.97/29.70 fresh(fresh(fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(X2, Y2), Z2), implies(implies(Z2, X2), implies(W2, X2))), implies(implies(Y, Z), implies(Y, Z)))), true, implies(implies(implies(X2, Y2), Z2), implies(implies(Z2, X2), implies(W2, X2))), implies(implies(Y, Z), implies(Y, Z))), true, implies(implies(implies(Y, Z), Y), implies(X, Y))), true, implies(implies(implies(X, Y), implies(Y, Z)), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(X, Y)), implies(implies(Z, S), implies(X, Y)))), true, implies(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z))))), true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 3 (condensed_detachment) }
% 226.97/29.70 fresh(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(X2, Y2), Z2), implies(implies(Z2, X2), implies(W2, X2)))), true, implies(implies(Y, Z), implies(Y, Z))), true, implies(implies(implies(Y, Z), Y), implies(X, Y))), true, implies(implies(implies(X, Y), implies(Y, Z)), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(X, Y)), implies(implies(Z, S), implies(X, Y)))), true, implies(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z))))), true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 4 (ic_JLukasiewicz) }
% 226.97/29.70 fresh(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(Y, Z), implies(Y, Z))), true, implies(implies(implies(Y, Z), Y), implies(X, Y))), true, implies(implies(implies(X, Y), implies(Y, Z)), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(X, Y)), implies(implies(Z, S), implies(X, Y)))), true, implies(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z))))), true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 1 (condensed_detachment) }
% 226.97/29.70 fresh(fresh(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(Y, Z), Y), implies(X, Y))), true, implies(implies(implies(X, Y), implies(Y, Z)), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(X, Y)), implies(implies(Z, S), implies(X, Y)))), true, implies(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z))))), true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 1 (condensed_detachment) }
% 226.97/29.70 fresh(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(X, Y), implies(Y, Z)), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(X, Y)), implies(implies(Z, S), implies(X, Y)))), true, implies(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z))))), true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 1 (condensed_detachment) }
% 226.97/29.70 fresh(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(X, Y), Z), implies(Y, Z)), implies(X, Y)), implies(implies(Z, S), implies(X, Y)))), true, implies(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z))))), true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 1 (condensed_detachment) }
% 226.97/29.70 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z))))), true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 1 (condensed_detachment) }
% 226.97/29.70 fresh(fresh(true, true, implies(implies(implies(Z, S), implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 2 (condensed_detachment) }
% 226.97/29.70 fresh(is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.70 = { by axiom 3 (condensed_detachment) }
% 226.97/29.70 fresh2(is_a_theorem(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W)))), true, implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.71 = { by axiom 4 (ic_JLukasiewicz) }
% 226.97/29.71 fresh2(true, true, implies(implies(implies(X, Y), Z), implies(Y, Z)))
% 226.97/29.71 = { by axiom 1 (condensed_detachment) }
% 226.97/29.71 true
% 226.97/29.71
% 226.97/29.71 Lemma 19: is_a_theorem(implies(X, implies(implies(Y, implies(Y, Z)), implies(Y, Z)))) = true.
% 226.97/29.71 Proof:
% 226.97/29.71 is_a_theorem(implies(X, implies(implies(Y, implies(Y, Z)), implies(Y, Z))))
% 226.97/29.71 = { by lemma 16 R->L }
% 226.97/29.71 fresh2(is_a_theorem(implies(implies(Y, implies(Y, Z)), implies(implies(Y, implies(Y, Z)), implies(Y, Z)))), true, implies(X, implies(implies(Y, implies(Y, Z)), implies(Y, Z))))
% 226.97/29.71 = { by lemma 15 }
% 226.97/29.71 fresh2(true, true, implies(X, implies(implies(Y, implies(Y, Z)), implies(Y, Z))))
% 226.97/29.71 = { by axiom 1 (condensed_detachment) }
% 226.97/29.71 true
% 226.97/29.71
% 226.97/29.71 Lemma 20: fresh2(is_a_theorem(implies(X, implies(X, Y))), true, implies(X, Y)) = is_a_theorem(implies(X, Y)).
% 226.97/29.71 Proof:
% 226.97/29.71 fresh2(is_a_theorem(implies(X, implies(X, Y))), true, implies(X, Y))
% 226.97/29.71 = { by axiom 3 (condensed_detachment) R->L }
% 226.97/29.71 fresh(is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))), true, implies(X, implies(X, Y)), implies(X, Y))
% 226.97/29.71 = { by lemma 17 R->L }
% 226.97/29.71 fresh(fresh2(is_a_theorem(implies(implies(Z, Z), implies(implies(X, implies(X, Y)), implies(X, Y)))), true, implies(implies(X, implies(X, Y)), implies(X, Y))), true, implies(X, implies(X, Y)), implies(X, Y))
% 226.97/29.71 = { by lemma 19 }
% 226.97/29.71 fresh(fresh2(true, true, implies(implies(X, implies(X, Y)), implies(X, Y))), true, implies(X, implies(X, Y)), implies(X, Y))
% 226.97/29.71 = { by axiom 1 (condensed_detachment) }
% 226.97/29.71 fresh(true, true, implies(X, implies(X, Y)), implies(X, Y))
% 226.97/29.71 = { by axiom 2 (condensed_detachment) }
% 226.97/29.77 is_a_theorem(implies(X, Y))
% 226.97/29.77
% 226.97/29.77 Goal 1 (prove_ic_5): is_a_theorem(implies(a, implies(implies(a, b), b))) = true.
% 226.97/29.77 Proof:
% 226.97/29.77 is_a_theorem(implies(a, implies(implies(a, b), b)))
% 226.97/29.77 = { by axiom 2 (condensed_detachment) R->L }
% 226.97/29.77 fresh(true, true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))
% 226.97/29.77 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.77 fresh(fresh2(true, true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))
% 226.97/29.77 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.77 fresh(fresh2(fresh2(true, true, implies(implies(X, X), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))
% 226.97/29.77 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.77 fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b))))), true, implies(implies(X, X), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))
% 226.97/29.77 = { by lemma 19 R->L }
% 226.97/29.77 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), Y), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b))))), true, implies(implies(X, X), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))
% 226.97/29.77 = { by lemma 5 }
% 226.97/29.77 fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b))))), true, implies(implies(X, X), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))
% 226.97/29.77 = { by lemma 16 }
% 226.97/29.77 fresh(fresh2(is_a_theorem(implies(implies(X, X), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))
% 226.97/29.77 = { by lemma 17 }
% 226.97/29.77 fresh(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(a, implies(implies(a, b), b)))
% 226.97/29.77 = { by axiom 3 (condensed_detachment) }
% 226.97/29.77 fresh2(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.77 = { by lemma 17 R->L }
% 226.97/29.77 fresh2(fresh2(is_a_theorem(implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.77 = { by axiom 2 (condensed_detachment) R->L }
% 226.97/29.77 fresh2(fresh2(fresh(true, true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.77 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.77 fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.77 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.77 fresh2(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), W), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.78 = { by lemma 18 R->L }
% 226.97/29.78 fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), b), V), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), W), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.78 = { by lemma 14 }
% 226.97/29.78 fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), W), implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.78 = { by lemma 5 }
% 226.97/29.78 fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.78 = { by axiom 3 (condensed_detachment) }
% 226.97/29.78 fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.78 = { by lemma 20 R->L }
% 226.97/29.78 fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.78 = { by lemma 5 R->L }
% 226.97/29.78 fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.78 = { by lemma 20 R->L }
% 226.97/29.79 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.79 = { by lemma 5 R->L }
% 226.97/29.79 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.79 = { by lemma 5 R->L }
% 226.97/29.79 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.79 = { by lemma 17 R->L }
% 226.97/29.79 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.80 = { by lemma 14 R->L }
% 226.97/29.80 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.80 = { by axiom 2 (condensed_detachment) R->L }
% 226.97/29.80 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 226.97/29.81 = { by axiom 1 (condensed_detachment) R->L }
% 226.97/29.81 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 227.50/29.82 = { by axiom 1 (condensed_detachment) R->L }
% 227.50/29.82 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 227.50/29.84 = { by axiom 1 (condensed_detachment) R->L }
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% 227.50/29.86 = { by axiom 1 (condensed_detachment) R->L }
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% 228.77/29.89 = { by axiom 1 (condensed_detachment) R->L }
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% 229.00/29.92 = { by axiom 1 (condensed_detachment) R->L }
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% 229.09/29.96 = { by axiom 1 (condensed_detachment) R->L }
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% 229.80/30.03 = { by axiom 1 (condensed_detachment) R->L }
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% 230.39/30.12 = { by axiom 1 (condensed_detachment) R->L }
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% 231.37/30.22 = { by axiom 1 (condensed_detachment) R->L }
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% 231.49/30.33 = { by axiom 1 (condensed_detachment) R->L }
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% 232.37/30.48 = { by axiom 1 (condensed_detachment) R->L }
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% 233.87/30.62 = { by axiom 1 (condensed_detachment) R->L }
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% 235.73/30.80 = { by axiom 1 (condensed_detachment) R->L }
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T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), 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implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 236.96/30.94 = { by lemma 9 R->L }
% 237.40/30.99 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(X2, X2), 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implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), 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implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 237.99/31.07 = { by lemma 5 }
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b), b)))))))), true, implies(implies(Z2, Z2), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), 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b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 237.99/31.19 = { by lemma 16 }
% 238.26/31.22 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(V2, V2), implies(implies(implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), 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implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 239.31/31.25 = { by lemma 17 }
% 239.53/31.28 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), 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implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 239.53/31.32 = { by lemma 5 }
% 240.06/31.34 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), 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implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 240.06/31.36 = { by lemma 16 }
% 240.32/31.38 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(W2, W2), implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(Z2, Z2), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), 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implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 240.32/31.40 = { by lemma 17 }
% 240.32/31.42 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), implies(implies(implies(implies(X2, X2), 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implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, 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implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 240.32/31.43 = { by lemma 14 }
% 240.90/31.44 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(Z2, Z2), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 240.90/31.45 = { by lemma 17 }
% 240.90/31.47 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 241.18/31.47 = { by lemma 5 }
% 241.18/31.48 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 241.18/31.49 = { by lemma 20 }
% 241.18/31.50 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 241.18/31.51 = { by lemma 5 }
% 241.18/31.51 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 241.18/31.53 = { by lemma 20 }
% 241.18/31.53 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 241.70/31.54 = { by axiom 3 (condensed_detachment) R->L }
% 241.70/31.55 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 241.70/31.56 = { by lemma 5 R->L }
% 241.92/31.56 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), U2), implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 241.92/31.57 = { by lemma 13 R->L }
% 241.92/31.58 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), U2), implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 241.92/31.59 = { by lemma 12 }
% 241.92/31.59 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), U2), implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))))), true, implies(implies(implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), 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% 241.92/31.60 = { by axiom 1 (condensed_detachment) }
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% 241.92/31.61 = { by axiom 1 (condensed_detachment) }
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b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 241.92/31.61 = { by axiom 2 (condensed_detachment) }
% 241.92/31.62 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(Y2, Y2), implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 241.92/31.62 = { by lemma 17 }
% 241.92/31.62 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 241.92/31.62 = { by axiom 3 (condensed_detachment) }
% 241.92/31.62 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.45/31.63 = { by lemma 14 R->L }
% 242.45/31.63 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.45/31.63 = { by lemma 5 R->L }
% 242.45/31.64 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(b, T), a)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.45/31.64 = { by lemma 5 R->L }
% 242.45/31.64 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(b, T), a), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(b, T), a)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.45/31.65 = { by lemma 5 R->L }
% 242.45/31.65 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), a), implies(implies(b, T), a))), true, implies(implies(implies(implies(b, T), a), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(b, T), a)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.45/31.65 = { by lemma 5 R->L }
% 242.45/31.66 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), a), implies(implies(b, T), a))), true, implies(implies(implies(implies(b, T), a), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(b, T), a)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.66 = { by axiom 2 (condensed_detachment) R->L }
% 242.70/31.67 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(implies(implies(a, b), b), S2), implies(a, implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), a), implies(implies(b, T), a))), true, implies(implies(implies(implies(b, T), a), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(b, T), a)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.67 = { by lemma 18 R->L }
% 242.70/31.67 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), b), S2), implies(a, implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(a, b), b), S2), implies(a, implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), a), implies(implies(b, T), a))), true, implies(implies(implies(implies(b, T), a), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(b, T), a)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.68 = { by axiom 3 (condensed_detachment) }
% 242.70/31.68 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), S2), implies(a, implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), a), implies(implies(b, T), a))), true, implies(implies(implies(implies(b, T), a), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(b, T), a)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.69 = { by axiom 4 (ic_JLukasiewicz) }
% 242.70/31.69 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), a), implies(implies(b, T), a))), true, implies(implies(implies(implies(b, T), a), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(b, T), a)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), 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implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.69 = { by axiom 1 (condensed_detachment) }
% 242.70/31.69 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))), a), implies(implies(b, T), a))), true, implies(implies(implies(implies(b, T), a), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(b, T), a)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.70 = { by axiom 1 (condensed_detachment) }
% 242.70/31.70 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(b, T), a), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), implies(implies(b, T), a)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), T2), implies(implies(b, T), a)), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), S), implies(implies(X2, X2), implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))))), true, implies(implies(implies(implies(b, T), a), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(U, U), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.70 = { by axiom 1 (condensed_detachment) }
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% 242.70/31.71 = { by axiom 1 (condensed_detachment) }
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% 242.70/31.71 = { by axiom 1 (condensed_detachment) }
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% 242.70/31.71 = { by axiom 1 (condensed_detachment) }
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% 242.70/31.72 = { by axiom 1 (condensed_detachment) }
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% 242.70/31.72 = { by axiom 1 (condensed_detachment) }
% 242.70/31.72 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.72 = { by axiom 1 (condensed_detachment) }
% 242.70/31.72 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.72 = { by axiom 1 (condensed_detachment) }
% 242.70/31.72 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.72 = { by axiom 1 (condensed_detachment) }
% 242.70/31.72 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b))), implies(implies(a, b), implies(implies(a, b), b)))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.72 = { by axiom 1 (condensed_detachment) }
% 242.70/31.72 fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.72 = { by axiom 1 (condensed_detachment) }
% 242.70/31.72 fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.72 = { by axiom 1 (condensed_detachment) }
% 242.70/31.72 fresh2(fresh2(fresh2(true, true, implies(implies(Z, Z), implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.72 = { by axiom 1 (condensed_detachment) }
% 242.70/31.73 fresh2(fresh2(true, true, implies(implies(implies(implies(a, b), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, implies(a, implies(implies(a, b), b)))
% 242.70/31.73 = { by axiom 1 (condensed_detachment) }
% 242.70/31.73 fresh2(true, true, implies(a, implies(implies(a, b), b)))
% 242.70/31.73 = { by axiom 1 (condensed_detachment) }
% 242.70/31.73 true
% 242.70/31.73 % SZS output end Proof
% 242.70/31.73
% 242.70/31.73 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------