TSTP Solution File: LCL093-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL093-1 : 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 : n022.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 08:17:23 EDT 2023
% Result : Unsatisfiable 77.68s 10.31s
% Output : Proof 82.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL093-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 00:40:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 77.68/10.31 Command-line arguments: --no-flatten-goal
% 77.68/10.31
% 77.68/10.31 % SZS status Unsatisfiable
% 77.68/10.31
% 79.82/10.54 % SZS output start Proof
% 79.82/10.54 Take the following subset of the input axioms:
% 79.82/10.54 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(implies(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 79.82/10.54 fof(ic_JLukasiewicz_5, axiom, ![P, Q, R, S, T]: is_a_theorem(implies(implies(implies(P, Q), implies(R, S)), implies(implies(S, P), implies(T, implies(R, P)))))).
% 79.82/10.54 fof(prove_ic_4, negated_conjecture, ~is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c))))).
% 79.82/10.54
% 79.82/10.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 79.82/10.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 79.82/10.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 79.82/10.54 fresh(y, y, x1...xn) = u
% 79.82/10.54 C => fresh(s, t, x1...xn) = v
% 79.82/10.54 where fresh is a fresh function symbol and x1..xn are the free
% 79.82/10.54 variables of u and v.
% 79.82/10.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 79.82/10.54 input problem has no model of domain size 1).
% 79.82/10.54
% 79.82/10.54 The encoding turns the above axioms into the following unit equations and goals:
% 79.82/10.54
% 79.82/10.54 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 79.82/10.54 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 79.82/10.54 Axiom 3 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 79.82/10.54 Axiom 4 (ic_JLukasiewicz_5): is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X))))) = true.
% 79.82/10.54
% 79.82/10.54 Lemma 5: fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, W))), true, implies(implies(W, X), implies(V, implies(Z, X)))) = is_a_theorem(implies(implies(W, X), implies(V, implies(Z, X)))).
% 79.82/10.54 Proof:
% 79.82/10.54 fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, W))), true, implies(implies(W, X), implies(V, implies(Z, X))))
% 79.82/10.54 = { by axiom 3 (condensed_detachment) R->L }
% 79.82/10.54 fresh(is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X))))), true, implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X))))
% 79.82/10.54 = { by axiom 4 (ic_JLukasiewicz_5) }
% 79.82/10.54 fresh(true, true, implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X))))
% 79.82/10.54 = { by axiom 2 (condensed_detachment) }
% 79.82/10.54 is_a_theorem(implies(implies(W, X), implies(V, implies(Z, X))))
% 79.82/10.55
% 79.82/10.55 Lemma 6: is_a_theorem(implies(implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W))))) = true.
% 79.82/10.55 Proof:
% 79.82/10.55 is_a_theorem(implies(implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W)))))
% 79.82/10.55 = { by lemma 5 R->L }
% 79.82/10.55 fresh2(is_a_theorem(implies(implies(implies(Z, W), implies(Y, U)), implies(implies(U, Z), implies(X, implies(Y, Z))))), true, implies(implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W)))))
% 79.82/10.55 = { by axiom 4 (ic_JLukasiewicz_5) }
% 79.82/10.55 fresh2(true, true, implies(implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W)))))
% 79.82/10.55 = { by axiom 1 (condensed_detachment) }
% 79.82/10.55 true
% 79.82/10.55
% 79.82/10.55 Lemma 7: fresh2(is_a_theorem(implies(implies(X, implies(Y, Z)), implies(Z, W))), true, implies(V, implies(implies(U, Z), implies(Z, W)))) = is_a_theorem(implies(V, implies(implies(U, Z), implies(Z, W)))).
% 79.82/10.55 Proof:
% 79.82/10.55 fresh2(is_a_theorem(implies(implies(X, implies(Y, Z)), implies(Z, W))), true, implies(V, implies(implies(U, Z), implies(Z, W))))
% 79.82/10.55 = { by axiom 3 (condensed_detachment) R->L }
% 79.82/10.55 fresh(is_a_theorem(implies(implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W))))), true, implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W))))
% 79.82/10.55 = { by lemma 6 }
% 79.82/10.55 fresh(true, true, implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W))))
% 79.82/10.55 = { by axiom 2 (condensed_detachment) }
% 79.82/10.55 is_a_theorem(implies(V, implies(implies(U, Z), implies(Z, W))))
% 79.82/10.55
% 79.82/10.55 Lemma 8: is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))) = true.
% 79.82/10.55 Proof:
% 79.82/10.55 is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))
% 79.82/10.55 = { by axiom 2 (condensed_detachment) R->L }
% 79.82/10.55 fresh(true, true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))
% 79.82/10.55 = { by axiom 1 (condensed_detachment) R->L }
% 79.82/10.55 fresh(fresh2(true, true, implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))
% 79.82/10.55 = { by lemma 6 R->L }
% 79.82/10.55 fresh(fresh2(is_a_theorem(implies(implies(implies(Y2, implies(Z2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y))))), true, implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))
% 79.82/10.55 = { by lemma 7 }
% 79.82/10.55 fresh(is_a_theorem(implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))
% 79.82/10.55 = { by axiom 3 (condensed_detachment) }
% 79.82/10.55 fresh2(is_a_theorem(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V))))), true, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))
% 79.82/10.55 = { by axiom 4 (ic_JLukasiewicz_5) }
% 79.82/10.55 fresh2(true, true, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))
% 79.82/10.55 = { by axiom 1 (condensed_detachment) }
% 79.82/10.55 true
% 79.82/10.55
% 79.82/10.55 Lemma 9: is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, Z)), W), implies(V, implies(Z, W)))) = true.
% 79.82/10.55 Proof:
% 79.82/10.55 is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, Z)), W), implies(V, implies(Z, W))))
% 79.82/10.55 = { by lemma 5 R->L }
% 79.82/10.55 fresh2(is_a_theorem(implies(implies(W, Z), implies(Z, implies(implies(X, Y), implies(Y, Z))))), true, implies(implies(implies(implies(X, Y), implies(Y, Z)), W), implies(V, implies(Z, W))))
% 79.82/10.55 = { by lemma 8 }
% 79.82/10.55 fresh2(true, true, implies(implies(implies(implies(X, Y), implies(Y, Z)), W), implies(V, implies(Z, W))))
% 79.82/10.55 = { by axiom 1 (condensed_detachment) }
% 79.82/10.55 true
% 79.82/10.55
% 79.82/10.55 Lemma 10: is_a_theorem(implies(implies(X, Y), implies(Y, implies(Z, implies(W, Y))))) = true.
% 79.82/10.55 Proof:
% 79.82/10.55 is_a_theorem(implies(implies(X, Y), implies(Y, implies(Z, implies(W, Y)))))
% 79.82/10.55 = { by axiom 2 (condensed_detachment) R->L }
% 79.82/10.55 fresh(true, true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(Z, implies(W, Y)))))
% 79.82/10.55 = { by axiom 1 (condensed_detachment) R->L }
% 79.82/10.55 fresh(fresh2(true, true, implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(Z, implies(W, Y)))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(Z, implies(W, Y)))))
% 79.82/10.55 = { by lemma 9 R->L }
% 79.82/10.55 fresh(fresh2(is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(Z2, Z)), implies(W, Y)), implies(Y, implies(Z, implies(W, Y))))), true, implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(Z, implies(W, Y)))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(Z, implies(W, Y)))))
% 79.82/10.55 = { by lemma 7 }
% 79.82/10.55 fresh(is_a_theorem(implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(Z, implies(W, Y)))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(X, Y), implies(Y, implies(Z, implies(W, Y)))))
% 79.82/10.55 = { by axiom 3 (condensed_detachment) }
% 79.82/10.55 fresh2(is_a_theorem(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V))))), true, implies(implies(X, Y), implies(Y, implies(Z, implies(W, Y)))))
% 79.82/10.55 = { by axiom 4 (ic_JLukasiewicz_5) }
% 79.82/10.55 fresh2(true, true, implies(implies(X, Y), implies(Y, implies(Z, implies(W, Y)))))
% 79.82/10.55 = { by axiom 1 (condensed_detachment) }
% 79.82/10.55 true
% 79.82/10.55
% 79.82/10.55 Lemma 11: is_a_theorem(implies(implies(implies(X, implies(Y, Z)), W), implies(V, implies(Z, W)))) = true.
% 79.82/10.55 Proof:
% 79.82/10.55 is_a_theorem(implies(implies(implies(X, implies(Y, Z)), W), implies(V, implies(Z, W))))
% 79.82/10.55 = { by lemma 5 R->L }
% 79.82/10.55 fresh2(is_a_theorem(implies(implies(W, Z), implies(Z, implies(X, implies(Y, Z))))), true, implies(implies(implies(X, implies(Y, Z)), W), implies(V, implies(Z, W))))
% 79.82/10.55 = { by lemma 10 }
% 79.82/10.55 fresh2(true, true, implies(implies(implies(X, implies(Y, Z)), W), implies(V, implies(Z, W))))
% 79.82/10.55 = { by axiom 1 (condensed_detachment) }
% 79.82/10.55 true
% 79.82/10.55
% 79.82/10.55 Lemma 12: fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, implies(W, X)))), true, implies(V, implies(U, implies(Z, implies(W, X))))) = is_a_theorem(implies(V, implies(U, implies(Z, implies(W, X))))).
% 79.82/10.55 Proof:
% 79.82/10.55 fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, implies(W, X)))), true, implies(V, implies(U, implies(Z, implies(W, X)))))
% 79.82/10.55 = { by axiom 3 (condensed_detachment) R->L }
% 79.82/10.55 fresh(is_a_theorem(implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 79.82/10.55 = { by lemma 5 R->L }
% 79.82/10.55 fresh(fresh2(is_a_theorem(implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 79.82/10.55 = { by lemma 11 }
% 79.82/10.55 fresh(fresh2(true, true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 79.82/10.55 = { by axiom 1 (condensed_detachment) }
% 79.82/10.55 fresh(true, true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 79.82/10.55 = { by axiom 2 (condensed_detachment) }
% 79.82/10.55 is_a_theorem(implies(V, implies(U, implies(Z, implies(W, X)))))
% 79.82/10.55
% 79.82/10.55 Lemma 13: is_a_theorem(implies(X, implies(Y, Y))) = true.
% 79.82/10.55 Proof:
% 79.82/10.55 is_a_theorem(implies(X, implies(Y, Y)))
% 79.82/10.55 = { by axiom 2 (condensed_detachment) R->L }
% 79.82/10.55 fresh(true, true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.55 = { by axiom 1 (condensed_detachment) R->L }
% 79.82/10.55 fresh(fresh2(true, true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.55 = { by axiom 4 (ic_JLukasiewicz_5) R->L }
% 79.82/10.55 fresh(fresh2(is_a_theorem(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S))))), true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.55 = { by axiom 3 (condensed_detachment) R->L }
% 79.82/10.55 fresh(fresh(is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.55 = { by lemma 12 R->L }
% 79.82/10.55 fresh(fresh(fresh2(is_a_theorem(implies(implies(Y, Y), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.55 = { by axiom 2 (condensed_detachment) R->L }
% 79.82/10.55 fresh(fresh(fresh2(fresh(true, true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.55 = { by axiom 1 (condensed_detachment) R->L }
% 79.82/10.55 fresh(fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.55 = { by axiom 4 (ic_JLukasiewicz_5) R->L }
% 79.82/10.56 fresh(fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(implies(V3, Y3), implies(U3, implies(W3, Y3))))), true, implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.56 = { by axiom 3 (condensed_detachment) R->L }
% 79.82/10.56 fresh(fresh(fresh2(fresh(fresh(is_a_theorem(implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(implies(V3, Y3), implies(U3, implies(W3, Y3)))), implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y)))))), true, implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(implies(V3, Y3), implies(U3, implies(W3, Y3)))), implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.56 = { by lemma 12 R->L }
% 79.82/10.56 fresh(fresh(fresh2(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(Y, Y), implies(Y, Y)), implies(implies(Y, Y), implies(X, implies(Y, Y))))), true, implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(implies(V3, Y3), implies(U3, implies(W3, Y3)))), implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y)))))), true, implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(implies(V3, Y3), implies(U3, implies(W3, Y3)))), implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.56 = { by axiom 4 (ic_JLukasiewicz_5) }
% 79.82/10.56 fresh(fresh(fresh2(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(implies(V3, Y3), implies(U3, implies(W3, Y3)))), implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y)))))), true, implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(implies(V3, Y3), implies(U3, implies(W3, Y3)))), implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.56 = { by axiom 1 (condensed_detachment) }
% 79.82/10.56 fresh(fresh(fresh2(fresh(fresh(true, true, implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(implies(V3, Y3), implies(U3, implies(W3, Y3)))), implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.56 = { by axiom 2 (condensed_detachment) }
% 79.82/10.56 fresh(fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(Y, Y), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.56 = { by axiom 3 (condensed_detachment) }
% 79.82/10.56 fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2))))), true, implies(implies(Y, Y), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.56 = { by axiom 4 (ic_JLukasiewicz_5) }
% 79.82/10.56 fresh(fresh(fresh2(fresh2(true, true, implies(implies(Y, Y), implies(X, implies(Y, Y)))), true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.56 = { by axiom 1 (condensed_detachment) }
% 79.82/10.56 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.56 = { by axiom 1 (condensed_detachment) }
% 79.82/10.56 fresh(fresh(true, true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.56 = { by axiom 2 (condensed_detachment) }
% 79.82/10.56 fresh(is_a_theorem(implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(X, implies(Y, Y)))
% 79.82/10.56 = { by axiom 3 (condensed_detachment) }
% 79.82/10.56 fresh2(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z))))), true, implies(X, implies(Y, Y)))
% 79.82/10.56 = { by axiom 4 (ic_JLukasiewicz_5) }
% 79.82/10.56 fresh2(true, true, implies(X, implies(Y, Y)))
% 79.82/10.56 = { by axiom 1 (condensed_detachment) }
% 79.82/10.56 true
% 79.82/10.56
% 79.82/10.56 Lemma 14: is_a_theorem(implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W)))) = true.
% 79.82/10.56 Proof:
% 79.82/10.56 is_a_theorem(implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.56 = { by lemma 5 R->L }
% 79.82/10.56 fresh2(is_a_theorem(implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.56 = { by axiom 2 (condensed_detachment) R->L }
% 79.82/10.56 fresh2(fresh(true, true, implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.56 = { by axiom 1 (condensed_detachment) R->L }
% 79.82/10.56 fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))))), true, implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.56 = { by axiom 1 (condensed_detachment) R->L }
% 79.82/10.56 fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), implies(Z, X)), implies(U, implies(implies(Y, implies(X, Y)), implies(Z, X))))), true, implies(implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))))), true, implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.56 = { by axiom 1 (condensed_detachment) R->L }
% 79.82/10.56 fresh2(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(Z, X), implies(Z, Y)), implies(implies(Y, implies(X, Y)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), implies(Z, X)), implies(U, implies(implies(Y, implies(X, Y)), implies(Z, X))))), true, implies(implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))))), true, implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.56 = { by lemma 9 R->L }
% 79.82/10.56 fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(S, X2), implies(X2, Z)), Y), implies(implies(Z, X), implies(Z, Y)))), true, implies(implies(implies(Z, X), implies(Z, Y)), implies(implies(Y, implies(X, Y)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), implies(Z, X)), implies(U, implies(implies(Y, implies(X, Y)), implies(Z, X))))), true, implies(implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))))), true, implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.56 = { by axiom 3 (condensed_detachment) R->L }
% 79.82/10.57 fresh2(fresh(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(S, X2), implies(X2, Z)), Y), implies(implies(Z, X), implies(Z, Y))), implies(implies(implies(Z, X), implies(Z, Y)), implies(implies(Y, implies(X, Y)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))))), true, implies(implies(implies(implies(S, X2), implies(X2, Z)), Y), implies(implies(Z, X), implies(Z, Y))), implies(implies(implies(Z, X), implies(Z, Y)), implies(implies(Y, implies(X, Y)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), implies(Z, X)), implies(U, implies(implies(Y, implies(X, Y)), implies(Z, X))))), true, implies(implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))))), true, implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.57 = { by lemma 8 }
% 79.82/10.57 fresh2(fresh(fresh2(fresh2(fresh(true, true, implies(implies(implies(implies(S, X2), implies(X2, Z)), Y), implies(implies(Z, X), implies(Z, Y))), implies(implies(implies(Z, X), implies(Z, Y)), implies(implies(Y, implies(X, Y)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), implies(Z, X)), implies(U, implies(implies(Y, implies(X, Y)), implies(Z, X))))), true, implies(implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))))), true, implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.57 = { by axiom 2 (condensed_detachment) }
% 79.82/10.57 fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(Z, X), implies(Z, Y)), implies(implies(Y, implies(X, Y)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), implies(Z, X)), implies(U, implies(implies(Y, implies(X, Y)), implies(Z, X))))), true, implies(implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))))), true, implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.57 = { by lemma 5 }
% 79.82/10.57 fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), implies(Z, X)), implies(U, implies(implies(Y, implies(X, Y)), implies(Z, X))))), true, implies(implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))))), true, implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.57 = { by lemma 5 }
% 79.82/10.57 fresh2(fresh(is_a_theorem(implies(implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))))), true, implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))), implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.57 = { by axiom 3 (condensed_detachment) }
% 79.82/10.57 fresh2(fresh2(is_a_theorem(implies(implies(implies(Y, implies(X, Y)), implies(Z, X)), implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))))), true, implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.57 = { by axiom 4 (ic_JLukasiewicz_5) }
% 79.82/10.57 fresh2(fresh2(true, true, implies(implies(W, T), implies(U, implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))))), true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.57 = { by axiom 1 (condensed_detachment) }
% 79.82/10.57 fresh2(true, true, implies(implies(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y))), W), implies(V, implies(U, W))))
% 79.82/10.57 = { by axiom 1 (condensed_detachment) }
% 79.82/10.57 true
% 79.82/10.57
% 79.82/10.57 Lemma 15: is_a_theorem(implies(X, implies(Y, implies(implies(Y, Z), implies(W, implies(V, Z)))))) = true.
% 79.82/10.57 Proof:
% 79.82/10.57 is_a_theorem(implies(X, implies(Y, implies(implies(Y, Z), implies(W, implies(V, Z))))))
% 79.82/10.57 = { by axiom 2 (condensed_detachment) R->L }
% 79.82/10.57 fresh(true, true, implies(implies(implies(Z, V), implies(V, Y)), implies(implies(Y, Z), implies(W, implies(V, Z)))), implies(X, implies(Y, implies(implies(Y, Z), implies(W, implies(V, Z))))))
% 79.82/10.57 = { by lemma 9 R->L }
% 79.82/10.57 fresh(is_a_theorem(implies(implies(implies(implies(Z, V), implies(V, Y)), implies(implies(Y, Z), implies(W, implies(V, Z)))), implies(X, implies(Y, implies(implies(Y, Z), implies(W, implies(V, Z))))))), true, implies(implies(implies(Z, V), implies(V, Y)), implies(implies(Y, Z), implies(W, implies(V, Z)))), implies(X, implies(Y, implies(implies(Y, Z), implies(W, implies(V, Z))))))
% 79.82/10.57 = { by axiom 3 (condensed_detachment) }
% 79.82/10.57 fresh2(is_a_theorem(implies(implies(implies(Z, V), implies(V, Y)), implies(implies(Y, Z), implies(W, implies(V, Z))))), true, implies(X, implies(Y, implies(implies(Y, Z), implies(W, implies(V, Z))))))
% 79.82/10.57 = { by axiom 4 (ic_JLukasiewicz_5) }
% 79.82/10.57 fresh2(true, true, implies(X, implies(Y, implies(implies(Y, Z), implies(W, implies(V, Z))))))
% 79.82/10.57 = { by axiom 1 (condensed_detachment) }
% 79.82/10.57 true
% 79.82/10.57
% 79.82/10.57 Lemma 16: is_a_theorem(implies(X, implies(implies(X, Y), implies(Z, implies(W, Y))))) = true.
% 79.82/10.57 Proof:
% 79.82/10.57 is_a_theorem(implies(X, implies(implies(X, Y), implies(Z, implies(W, Y)))))
% 79.82/10.57 = { by axiom 2 (condensed_detachment) R->L }
% 79.82/10.57 fresh(true, true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(X, implies(implies(X, Y), implies(Z, implies(W, Y)))))
% 79.82/10.57 = { by lemma 15 R->L }
% 79.82/10.57 fresh(is_a_theorem(implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(X, implies(implies(X, Y), implies(Z, implies(W, Y)))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(X, implies(implies(X, Y), implies(Z, implies(W, Y)))))
% 79.82/10.57 = { by axiom 3 (condensed_detachment) }
% 79.82/10.57 fresh2(is_a_theorem(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V))))), true, implies(X, implies(implies(X, Y), implies(Z, implies(W, Y)))))
% 79.82/10.57 = { by axiom 4 (ic_JLukasiewicz_5) }
% 79.82/10.57 fresh2(true, true, implies(X, implies(implies(X, Y), implies(Z, implies(W, Y)))))
% 79.82/10.57 = { by axiom 1 (condensed_detachment) }
% 79.82/10.57 true
% 79.82/10.57
% 79.82/10.57 Lemma 17: fresh2(is_a_theorem(implies(implies(X, implies(Y, Z)), W)), true, implies(V, implies(implies(implies(W, U), Z), W))) = is_a_theorem(implies(V, implies(implies(implies(W, U), Z), W))).
% 79.82/10.57 Proof:
% 79.82/10.57 fresh2(is_a_theorem(implies(implies(X, implies(Y, Z)), W)), true, implies(V, implies(implies(implies(W, U), Z), W)))
% 79.82/10.57 = { by axiom 3 (condensed_detachment) R->L }
% 79.82/10.57 fresh(is_a_theorem(implies(implies(implies(X, implies(Y, Z)), W), implies(V, implies(implies(implies(W, U), Z), W)))), true, implies(implies(X, implies(Y, Z)), W), implies(V, implies(implies(implies(W, U), Z), W)))
% 79.82/10.57 = { by lemma 5 R->L }
% 79.82/10.57 fresh(fresh2(is_a_theorem(implies(implies(W, U), implies(implies(implies(W, U), Z), implies(X, implies(Y, Z))))), true, implies(implies(implies(X, implies(Y, Z)), W), implies(V, implies(implies(implies(W, U), Z), W)))), true, implies(implies(X, implies(Y, Z)), W), implies(V, implies(implies(implies(W, U), Z), W)))
% 79.82/10.57 = { by lemma 16 }
% 79.82/10.57 fresh(fresh2(true, true, implies(implies(implies(X, implies(Y, Z)), W), implies(V, implies(implies(implies(W, U), Z), W)))), true, implies(implies(X, implies(Y, Z)), W), implies(V, implies(implies(implies(W, U), Z), W)))
% 79.82/10.57 = { by axiom 1 (condensed_detachment) }
% 79.82/10.57 fresh(true, true, implies(implies(X, implies(Y, Z)), W), implies(V, implies(implies(implies(W, U), Z), W)))
% 79.82/10.57 = { by axiom 2 (condensed_detachment) }
% 79.82/10.57 is_a_theorem(implies(V, implies(implies(implies(W, U), Z), W)))
% 79.82/10.57
% 79.82/10.57 Lemma 18: fresh2(is_a_theorem(implies(implies(implies(X, implies(Y, implies(Z, W))), V), W)), true, implies(X, implies(Y, implies(Z, W)))) = is_a_theorem(implies(X, implies(Y, implies(Z, W)))).
% 79.82/10.57 Proof:
% 80.12/10.57 fresh2(is_a_theorem(implies(implies(implies(X, implies(Y, implies(Z, W))), V), W)), true, implies(X, implies(Y, implies(Z, W))))
% 80.12/10.57 = { by axiom 3 (condensed_detachment) R->L }
% 80.12/10.57 fresh(is_a_theorem(implies(implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))), true, implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))
% 80.12/10.57 = { by axiom 2 (condensed_detachment) R->L }
% 80.12/10.57 fresh(fresh(true, true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))), true, implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))
% 80.12/10.57 = { by axiom 1 (condensed_detachment) R->L }
% 80.12/10.57 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W)))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))), true, implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))
% 80.12/10.57 = { by lemma 9 R->L }
% 80.12/10.57 fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(Z2, W2), implies(W2, Y)), implies(Z, W)), implies(X, implies(Y, implies(Z, W))))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W)))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))), true, implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))
% 80.12/10.57 = { by lemma 17 }
% 80.12/10.57 fresh(fresh(is_a_theorem(implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W)))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))), true, implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))
% 80.12/10.57 = { by axiom 3 (condensed_detachment) }
% 80.12/10.57 fresh(fresh2(is_a_theorem(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U))))), true, implies(implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))), true, implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))
% 80.12/10.57 = { by axiom 4 (ic_JLukasiewicz_5) }
% 80.12/10.57 fresh(fresh2(true, true, implies(implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))), true, implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))
% 80.12/10.57 = { by axiom 1 (condensed_detachment) }
% 80.12/10.57 fresh(true, true, implies(implies(implies(X, implies(Y, implies(Z, W))), V), W), implies(X, implies(Y, implies(Z, W))))
% 80.12/10.57 = { by axiom 2 (condensed_detachment) }
% 80.12/10.57 is_a_theorem(implies(X, implies(Y, implies(Z, W))))
% 80.12/10.57
% 80.12/10.57 Lemma 19: fresh2(is_a_theorem(implies(implies(implies(X, Y), Z), Y)), true, implies(W, implies(X, Y))) = is_a_theorem(implies(W, implies(X, Y))).
% 80.12/10.57 Proof:
% 80.12/10.57 fresh2(is_a_theorem(implies(implies(implies(X, Y), Z), Y)), true, implies(W, implies(X, Y)))
% 80.12/10.57 = { by axiom 3 (condensed_detachment) R->L }
% 80.12/10.57 fresh(is_a_theorem(implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))), true, implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))
% 80.12/10.57 = { by axiom 2 (condensed_detachment) R->L }
% 80.12/10.57 fresh(fresh(true, true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))), true, implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))
% 80.12/10.57 = { by axiom 1 (condensed_detachment) R->L }
% 80.12/10.57 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))), true, implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))
% 80.12/10.57 = { by axiom 4 (ic_JLukasiewicz_5) R->L }
% 80.12/10.57 fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(implies(V2, Y2), implies(U2, implies(W2, Y2))))), true, implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))), true, implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))
% 80.12/10.57 = { by axiom 3 (condensed_detachment) R->L }
% 80.12/10.58 fresh(fresh(fresh(is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(implies(V2, Y2), implies(U2, implies(W2, Y2)))), implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))))), true, implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(implies(V2, Y2), implies(U2, implies(W2, Y2)))), implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))), true, implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))
% 80.12/10.58 = { by lemma 12 R->L }
% 80.12/10.58 fresh(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y))))), true, implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(implies(V2, Y2), implies(U2, implies(W2, Y2)))), implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))))), true, implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(implies(V2, Y2), implies(U2, implies(W2, Y2)))), implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))), true, implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))
% 80.12/10.58 = { by lemma 16 }
% 80.12/10.58 fresh(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(implies(V2, Y2), implies(U2, implies(W2, Y2)))), implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))))), true, implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(implies(V2, Y2), implies(U2, implies(W2, Y2)))), implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))), true, implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))
% 80.12/10.58 = { by axiom 1 (condensed_detachment) }
% 80.12/10.58 fresh(fresh(fresh(true, true, implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(implies(V2, Y2), implies(U2, implies(W2, Y2)))), implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))), true, implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))
% 80.12/10.58 = { by axiom 2 (condensed_detachment) }
% 80.12/10.58 fresh(fresh(is_a_theorem(implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))), true, implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))
% 80.12/10.58 = { by axiom 3 (condensed_detachment) }
% 80.12/10.58 fresh(fresh2(is_a_theorem(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V))))), true, implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))), true, implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))
% 80.12/10.58 = { by axiom 4 (ic_JLukasiewicz_5) }
% 80.12/10.58 fresh(fresh2(true, true, implies(implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))), true, implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))
% 80.12/10.58 = { by axiom 1 (condensed_detachment) }
% 80.12/10.58 fresh(true, true, implies(implies(implies(X, Y), Z), Y), implies(W, implies(X, Y)))
% 80.12/10.58 = { by axiom 2 (condensed_detachment) }
% 80.12/10.58 is_a_theorem(implies(W, implies(X, Y)))
% 80.12/10.58
% 80.12/10.58 Lemma 20: fresh2(is_a_theorem(implies(implies(X, X), Y)), true, Y) = is_a_theorem(Y).
% 80.12/10.58 Proof:
% 80.12/10.58 fresh2(is_a_theorem(implies(implies(X, X), Y)), true, Y)
% 80.12/10.58 = { by axiom 3 (condensed_detachment) R->L }
% 80.12/10.58 fresh(is_a_theorem(implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.58 = { by axiom 2 (condensed_detachment) R->L }
% 80.12/10.58 fresh(fresh(true, true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.58 = { by axiom 1 (condensed_detachment) R->L }
% 80.12/10.58 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.58 = { by axiom 1 (condensed_detachment) R->L }
% 80.12/10.58 fresh(fresh(fresh2(fresh2(true, true, implies(X, X)), true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.58 = { by axiom 4 (ic_JLukasiewicz_5) R->L }
% 80.12/10.58 fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S))))), true, implies(X, X)), true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.58 = { by axiom 3 (condensed_detachment) R->L }
% 80.12/10.58 fresh(fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(X, X))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(X, X)), true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.58 = { by lemma 13 }
% 80.12/10.58 fresh(fresh(fresh2(fresh(true, true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(X, X)), true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.58 = { by axiom 2 (condensed_detachment) }
% 80.12/10.58 fresh(fresh(fresh2(is_a_theorem(implies(X, X)), true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.58 = { by axiom 3 (condensed_detachment) R->L }
% 80.12/10.58 fresh(fresh(fresh(is_a_theorem(implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.58 = { by axiom 2 (condensed_detachment) R->L }
% 80.12/10.58 fresh(fresh(fresh(fresh(true, true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.58 = { by axiom 1 (condensed_detachment) R->L }
% 80.12/10.58 fresh(fresh(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.58 = { by axiom 1 (condensed_detachment) R->L }
% 80.12/10.58 fresh(fresh(fresh(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), Y), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.59 = { by axiom 1 (condensed_detachment) R->L }
% 80.12/10.59 fresh(fresh(fresh(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(Y, implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), implies(implies(implies(X, X), Y), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))))), true, implies(implies(implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), Y), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.59 = { by lemma 14 R->L }
% 80.12/10.59 fresh(fresh(fresh(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(Y, implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), implies(implies(implies(X, X), Y), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))))), Y), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(implies(Y, implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), implies(implies(implies(X, X), Y), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))))), true, implies(implies(implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), Y), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.59 = { by lemma 18 }
% 80.12/10.59 fresh(fresh(fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(Y, implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), implies(implies(implies(X, X), Y), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))))), true, implies(implies(implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), Y), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.59 = { by lemma 5 }
% 80.12/10.59 fresh(fresh(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), Y), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.59 = { by lemma 19 }
% 80.12/10.59 fresh(fresh(fresh(fresh(is_a_theorem(implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.59 = { by axiom 3 (condensed_detachment) }
% 80.12/10.59 fresh(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2))))), true, implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.59 = { by axiom 4 (ic_JLukasiewicz_5) }
% 80.12/10.59 fresh(fresh(fresh(fresh2(true, true, implies(implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)))), true, implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.59 = { by axiom 1 (condensed_detachment) }
% 80.12/10.59 fresh(fresh(fresh(true, true, implies(X, X), implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.59 = { by axiom 2 (condensed_detachment) }
% 80.12/10.59 fresh(fresh(is_a_theorem(implies(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y))), true, implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z)))), implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.59 = { by axiom 3 (condensed_detachment) }
% 80.12/10.59 fresh(fresh2(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(implies(U, Z), implies(T, implies(V, Z))))), true, implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.59 = { by axiom 4 (ic_JLukasiewicz_5) }
% 80.12/10.59 fresh(fresh2(true, true, implies(implies(implies(X, X), Y), Y)), true, implies(implies(X, X), Y), Y)
% 80.12/10.59 = { by axiom 1 (condensed_detachment) }
% 80.12/10.59 fresh(true, true, implies(implies(X, X), Y), Y)
% 80.12/10.59 = { by axiom 2 (condensed_detachment) }
% 80.12/10.59 is_a_theorem(Y)
% 80.12/10.59
% 80.12/10.59 Lemma 21: is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, implies(W, Y))), V), implies(U, implies(X, V)))) = true.
% 80.12/10.59 Proof:
% 80.12/10.59 is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, implies(W, Y))), V), implies(U, implies(X, V))))
% 80.12/10.59 = { by lemma 5 R->L }
% 80.12/10.59 fresh2(is_a_theorem(implies(implies(V, T), implies(X, implies(implies(X, Y), implies(Z, implies(W, Y)))))), true, implies(implies(implies(implies(X, Y), implies(Z, implies(W, Y))), V), implies(U, implies(X, V))))
% 80.12/10.59 = { by lemma 15 }
% 80.12/10.59 fresh2(true, true, implies(implies(implies(implies(X, Y), implies(Z, implies(W, Y))), V), implies(U, implies(X, V))))
% 80.12/10.59 = { by axiom 1 (condensed_detachment) }
% 80.12/10.59 true
% 80.12/10.59
% 80.12/10.59 Lemma 22: is_a_theorem(implies(implies(implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))), implies(X, V)), implies(U, implies(T, implies(X, V))))) = true.
% 80.12/10.59 Proof:
% 80.12/10.59 is_a_theorem(implies(implies(implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))), implies(X, V)), implies(U, implies(T, implies(X, V)))))
% 80.12/10.59 = { by lemma 5 R->L }
% 80.12/10.59 fresh2(is_a_theorem(implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))), true, implies(implies(implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))), implies(X, V)), implies(U, implies(T, implies(X, V)))))
% 80.12/10.59 = { by lemma 18 R->L }
% 80.12/10.59 fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))))), W), implies(Y, implies(Z, W)))), true, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))), true, implies(implies(implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))), implies(X, V)), implies(U, implies(T, implies(X, V)))))
% 80.12/10.59 = { by lemma 5 R->L }
% 80.12/10.59 fresh2(fresh2(fresh2(is_a_theorem(implies(implies(W, S), implies(Z, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))))), true, implies(implies(implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))))), W), implies(Y, implies(Z, W)))), true, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))), true, implies(implies(implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))), implies(X, V)), implies(U, implies(T, implies(X, V)))))
% 80.12/10.59 = { by axiom 2 (condensed_detachment) R->L }
% 80.12/10.59 fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(implies(Y, implies(Z, W)), V), implies(implies(X, implies(Y, implies(Z, W))), implies(X, V))), implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))), implies(implies(W, S), implies(Z, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))))), true, implies(implies(implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))))), W), implies(Y, implies(Z, W)))), true, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))), true, implies(implies(implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))), implies(X, V)), implies(U, implies(T, implies(X, V)))))
% 80.12/10.60 = { by lemma 14 R->L }
% 80.12/10.60 fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(Y, implies(Z, W)), V), implies(implies(X, implies(Y, implies(Z, W))), implies(X, V))), implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))), implies(implies(W, S), implies(Z, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))))))))), true, implies(implies(implies(implies(Y, implies(Z, W)), V), implies(implies(X, implies(Y, implies(Z, W))), implies(X, V))), implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))), implies(implies(W, S), implies(Z, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))))), true, implies(implies(implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))))), W), implies(Y, implies(Z, W)))), true, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))), true, implies(implies(implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))), implies(X, V)), implies(U, implies(T, implies(X, V)))))
% 80.12/10.60 = { by axiom 3 (condensed_detachment) }
% 80.12/10.60 fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(Y, implies(Z, W)), V), implies(implies(X, implies(Y, implies(Z, W))), implies(X, V))), implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))))))), true, implies(implies(W, S), implies(Z, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))))), true, implies(implies(implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))))), W), implies(Y, implies(Z, W)))), true, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))), true, implies(implies(implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))), implies(X, V)), implies(U, implies(T, implies(X, V)))))
% 80.12/10.60 = { by axiom 4 (ic_JLukasiewicz_5) }
% 80.12/10.60 fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(W, S), implies(Z, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))))), true, implies(implies(implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))))), W), implies(Y, implies(Z, W)))), true, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))), true, implies(implies(implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))), implies(X, V)), implies(U, implies(T, implies(X, V)))))
% 80.12/10.60 = { by axiom 1 (condensed_detachment) }
% 80.12/10.60 fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))))), W), implies(Y, implies(Z, W)))), true, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))), true, implies(implies(implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))), implies(X, V)), implies(U, implies(T, implies(X, V)))))
% 80.12/10.60 = { by axiom 1 (condensed_detachment) }
% 80.12/10.60 fresh2(fresh2(true, true, implies(implies(implies(X, V), implies(Y, implies(Z, W))), implies(T, implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W)))))), true, implies(implies(implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))), implies(X, V)), implies(U, implies(T, implies(X, V)))))
% 80.12/10.60 = { by axiom 1 (condensed_detachment) }
% 80.12/10.60 fresh2(true, true, implies(implies(implies(implies(X, implies(Y, implies(Z, W))), implies(Y, implies(Z, W))), implies(X, V)), implies(U, implies(T, implies(X, V)))))
% 80.12/10.60 = { by axiom 1 (condensed_detachment) }
% 80.12/10.60 true
% 80.12/10.60
% 80.12/10.60 Lemma 23: fresh2(is_a_theorem(implies(X, implies(Y, implies(Z, implies(W, implies(V, implies(X, U))))))), true, implies(Y, implies(Z, implies(W, implies(V, implies(X, U)))))) = is_a_theorem(implies(Y, implies(Z, implies(W, implies(V, implies(X, U)))))).
% 80.12/10.60 Proof:
% 80.12/10.60 fresh2(is_a_theorem(implies(X, implies(Y, implies(Z, implies(W, implies(V, implies(X, U))))))), true, implies(Y, implies(Z, implies(W, implies(V, implies(X, U))))))
% 80.12/10.60 = { by axiom 3 (condensed_detachment) R->L }
% 80.12/10.60 fresh(is_a_theorem(implies(implies(X, implies(Y, implies(Z, implies(W, implies(V, implies(X, U)))))), implies(Y, implies(Z, implies(W, implies(V, implies(X, U))))))), true, implies(X, implies(Y, implies(Z, implies(W, implies(V, implies(X, U)))))), implies(Y, implies(Z, implies(W, implies(V, implies(X, U))))))
% 80.12/10.60 = { by lemma 18 R->L }
% 80.12/10.60 fresh(fresh2(is_a_theorem(implies(implies(implies(implies(X, implies(Y, implies(Z, implies(W, implies(V, implies(X, U)))))), implies(Y, implies(Z, implies(W, implies(V, implies(X, U)))))), implies(X, U)), implies(W, implies(V, implies(X, U))))), true, implies(implies(X, implies(Y, implies(Z, implies(W, implies(V, implies(X, U)))))), implies(Y, implies(Z, implies(W, implies(V, implies(X, U))))))), true, implies(X, implies(Y, implies(Z, implies(W, implies(V, implies(X, U)))))), implies(Y, implies(Z, implies(W, implies(V, implies(X, U))))))
% 80.12/10.60 = { by lemma 22 }
% 80.12/10.60 fresh(fresh2(true, true, implies(implies(X, implies(Y, implies(Z, implies(W, implies(V, implies(X, U)))))), implies(Y, implies(Z, implies(W, implies(V, implies(X, U))))))), true, implies(X, implies(Y, implies(Z, implies(W, implies(V, implies(X, U)))))), implies(Y, implies(Z, implies(W, implies(V, implies(X, U))))))
% 80.12/10.60 = { by axiom 1 (condensed_detachment) }
% 80.12/10.60 fresh(true, true, implies(X, implies(Y, implies(Z, implies(W, implies(V, implies(X, U)))))), implies(Y, implies(Z, implies(W, implies(V, implies(X, U))))))
% 80.12/10.60 = { by axiom 2 (condensed_detachment) }
% 80.12/10.61 is_a_theorem(implies(Y, implies(Z, implies(W, implies(V, implies(X, U))))))
% 80.12/10.61
% 80.12/10.61 Goal 1 (prove_ic_4): is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))) = true.
% 80.12/10.61 Proof:
% 80.12/10.61 is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.61 = { by axiom 2 (condensed_detachment) R->L }
% 80.12/10.61 fresh(true, true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.61 = { by axiom 1 (condensed_detachment) R->L }
% 80.12/10.61 fresh(fresh2(true, true, implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.61 = { by axiom 1 (condensed_detachment) R->L }
% 80.12/10.61 fresh(fresh2(fresh2(true, true, implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.61 = { by axiom 1 (condensed_detachment) R->L }
% 80.12/10.61 fresh(fresh2(fresh2(fresh2(true, true, implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.61 = { by lemma 22 R->L }
% 80.12/10.61 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.62 = { by axiom 3 (condensed_detachment) R->L }
% 80.12/10.62 fresh(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.62 = { by lemma 5 R->L }
% 80.12/10.62 fresh(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(X, X), implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.62 = { by lemma 5 R->L }
% 80.12/10.62 fresh(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), Z), implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(X, X), implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.62 = { by lemma 13 }
% 80.12/10.62 fresh(fresh2(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(X, X), implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.62 = { by axiom 1 (condensed_detachment) }
% 80.12/10.62 fresh(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.62 = { by axiom 1 (condensed_detachment) }
% 80.12/10.62 fresh(fresh2(fresh2(fresh(true, true, implies(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(a, c))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.62 = { by axiom 2 (condensed_detachment) }
% 80.12/10.63 fresh(fresh2(fresh2(is_a_theorem(implies(implies(Y, Y), implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.63 = { by lemma 20 }
% 80.12/10.63 fresh(fresh2(is_a_theorem(implies(implies(X, X), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.63 = { by lemma 20 }
% 80.12/10.63 fresh(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.63 = { by axiom 3 (condensed_detachment) }
% 80.12/10.63 fresh2(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.63 = { by lemma 20 R->L }
% 80.12/10.63 fresh2(fresh2(is_a_theorem(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.63 = { by lemma 23 R->L }
% 80.12/10.63 fresh2(fresh2(fresh2(is_a_theorem(implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.63 = { by axiom 2 (condensed_detachment) R->L }
% 80.12/10.63 fresh2(fresh2(fresh2(fresh(true, true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.63 = { by axiom 1 (condensed_detachment) R->L }
% 80.12/10.63 fresh2(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.12/10.63 = { by axiom 1 (condensed_detachment) R->L }
% 80.12/10.63 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.59/10.63 = { by axiom 1 (condensed_detachment) R->L }
% 80.59/10.63 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.59/10.64 = { by axiom 1 (condensed_detachment) R->L }
% 80.59/10.64 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.59/10.64 = { by lemma 21 R->L }
% 80.59/10.64 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.59/10.65 = { by axiom 3 (condensed_detachment) R->L }
% 80.59/10.65 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.59/10.65 = { by axiom 2 (condensed_detachment) R->L }
% 80.59/10.65 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh(true, true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.59/10.66 = { by axiom 1 (condensed_detachment) R->L }
% 80.79/10.66 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.79/10.66 = { by axiom 1 (condensed_detachment) R->L }
% 80.79/10.67 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh(fresh2(fresh2(true, true, implies(implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.79/10.67 = { by lemma 9 R->L }
% 80.79/10.68 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(Z2, implies(W, W))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.79/10.68 = { by axiom 3 (condensed_detachment) R->L }
% 80.79/10.68 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(Y2, Z2), implies(Z2, implies(W, W))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(implies(Y2, Z2), implies(Z2, implies(W, W))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.79/10.69 = { by lemma 10 }
% 80.79/10.69 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh(fresh2(fresh(true, true, implies(implies(implies(implies(Y2, Z2), implies(Z2, implies(W, W))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.79/10.69 = { by axiom 2 (condensed_detachment) }
% 80.79/10.70 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh(fresh2(is_a_theorem(implies(implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.79/10.70 = { by lemma 17 }
% 80.79/10.70 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh(is_a_theorem(implies(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.79/10.70 = { by axiom 3 (condensed_detachment) }
% 80.79/10.71 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(V, U), implies(T, S)), implies(implies(S, V), implies(X2, implies(T, V))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.79/10.71 = { by axiom 4 (ic_JLukasiewicz_5) }
% 80.79/10.71 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.79/10.71 = { by axiom 1 (condensed_detachment) }
% 80.79/10.71 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.79/10.72 = { by axiom 2 (condensed_detachment) }
% 80.79/10.72 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 80.79/10.72 = { by axiom 3 (condensed_detachment) R->L }
% 81.32/10.72 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 81.32/10.73 = { by lemma 18 R->L }
% 81.32/10.73 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 81.32/10.73 = { by lemma 5 R->L }
% 81.32/10.74 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 81.32/10.74 = { by axiom 2 (condensed_detachment) R->L }
% 81.32/10.75 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh(true, true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 81.32/10.75 = { by axiom 1 (condensed_detachment) R->L }
% 81.32/10.76 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 81.61/10.76 = { by lemma 21 R->L }
% 81.61/10.77 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(a, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 81.61/10.77 = { by lemma 5 }
% 81.61/10.78 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 81.61/10.78 = { by axiom 3 (condensed_detachment) }
% 81.61/10.79 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))), true, implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 81.61/10.80 = { by axiom 2 (condensed_detachment) R->L }
% 81.61/10.80 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))), true, implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 81.61/10.81 = { by axiom 1 (condensed_detachment) R->L }
% 81.61/10.81 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))), true, implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 81.61/10.82 = { by lemma 9 R->L }
% 81.61/10.82 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(Y3, Z3), implies(Z3, implies(b, c))), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))), true, implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))), true, implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 81.61/10.83 = { by axiom 3 (condensed_detachment) R->L }
% 82.20/10.84 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh(is_a_theorem(implies(implies(implies(implies(implies(Y3, Z3), implies(Z3, implies(b, c))), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))))), true, implies(implies(implies(implies(Y3, Z3), implies(Z3, implies(b, c))), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))), true, implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.20/10.84 = { by lemma 11 }
% 82.20/10.85 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh(true, true, implies(implies(implies(implies(Y3, Z3), implies(Z3, implies(b, c))), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))), true, implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.20/10.85 = { by axiom 2 (condensed_detachment) }
% 82.20/10.86 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2)))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))), true, implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.20/10.86 = { by axiom 3 (condensed_detachment) }
% 82.20/10.87 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(V2, U2), implies(T2, S2)), implies(implies(S2, V2), implies(X3, implies(T2, V2))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))), true, implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.20/10.87 = { by axiom 4 (ic_JLukasiewicz_5) }
% 82.49/10.87 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))))), true, implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.88 = { by axiom 1 (condensed_detachment) }
% 82.49/10.88 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), W2), implies(a, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.88 = { by axiom 1 (condensed_detachment) }
% 82.49/10.88 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.88 = { by axiom 1 (condensed_detachment) }
% 82.49/10.89 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.89 = { by axiom 1 (condensed_detachment) }
% 82.49/10.89 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(true, true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.89 = { by axiom 2 (condensed_detachment) }
% 82.49/10.89 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.89 = { by lemma 23 }
% 82.49/10.89 fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.89 = { by lemma 23 }
% 82.49/10.89 fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.89 = { by axiom 3 (condensed_detachment) }
% 82.49/10.89 fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.89 = { by lemma 23 R->L }
% 82.49/10.89 fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.89 = { by axiom 2 (condensed_detachment) R->L }
% 82.49/10.89 fresh2(fresh2(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(implies(a, b), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(b, c), implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.89 = { by lemma 21 R->L }
% 82.49/10.89 fresh2(fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(b, c), implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, implies(implies(implies(implies(a, b), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(b, c), implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.89 = { by axiom 3 (condensed_detachment) }
% 82.49/10.89 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.89 = { by lemma 5 R->L }
% 82.49/10.90 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), W3), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.90 = { by lemma 19 R->L }
% 82.49/10.90 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, b), implies(a, c))), c), implies(implies(a, b), implies(a, c)))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), W3), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.90 = { by lemma 14 }
% 82.49/10.90 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), W3), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.90 = { by axiom 1 (condensed_detachment) }
% 82.49/10.90 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(a, b), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.90 = { by axiom 1 (condensed_detachment) }
% 82.49/10.90 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(b, c), implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.90 = { by axiom 1 (condensed_detachment) }
% 82.49/10.90 fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(a, b), implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.90 = { by axiom 1 (condensed_detachment) }
% 82.49/10.90 fresh2(fresh2(fresh2(fresh2(true, true, implies(a, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.90 = { by axiom 1 (condensed_detachment) }
% 82.49/10.90 fresh2(fresh2(fresh2(true, true, implies(implies(W, W), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.90 = { by axiom 1 (condensed_detachment) }
% 82.49/10.90 fresh2(fresh2(true, true, implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.90 = { by axiom 1 (condensed_detachment) }
% 82.49/10.90 fresh2(true, true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 82.49/10.90 = { by axiom 1 (condensed_detachment) }
% 82.49/10.90 true
% 82.49/10.90 % SZS output end Proof
% 82.49/10.90
% 82.49/10.90 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------