%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL017-1 : 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 : n007.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 08:17:03 EDT 2023

% Result   : Timeout 289.53s 37.25s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL017-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13  % 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 : n007.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 : Thu Aug 24 17:38:10 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 289.53/37.25  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 289.53/37.25  
% 289.53/37.25  % SZS status Unsatisfiable
% 289.53/37.25  
% 290.33/37.32  % SZS output start Proof
% 290.33/37.32  Take the following subset of the input axioms:
% 290.33/37.32    fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 290.33/37.32    fof(prove_yro, negated_conjecture, ~is_a_theorem(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))).
% 290.33/37.32    fof(pyo, axiom, ![Z, X2, Y2]: is_a_theorem(equivalent(equivalent(equivalent(X2, equivalent(Y2, Z)), Z), equivalent(Y2, X2)))).
% 290.33/37.32  
% 290.33/37.32  Now clausify the problem and encode Horn clauses using encoding 3 of
% 290.33/37.32  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 290.33/37.32  We repeatedly replace C & s=t => u=v by the two clauses:
% 290.33/37.32    fresh(y, y, x1...xn) = u
% 290.33/37.32    C => fresh(s, t, x1...xn) = v
% 290.33/37.32  where fresh is a fresh function symbol and x1..xn are the free
% 290.33/37.32  variables of u and v.
% 290.33/37.33  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 290.33/37.33  input problem has no model of domain size 1).
% 290.33/37.33  
% 290.33/37.33  The encoding turns the above axioms into the following unit equations and goals:
% 290.33/37.33  
% 290.33/37.33  Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 290.33/37.33  Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 290.33/37.33  Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 290.33/37.33  Axiom 4 (pyo): is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), Z), equivalent(Y, X))) = true.
% 290.33/37.33  
% 290.33/37.33  Lemma 5: fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), Z)), true, equivalent(Y, X)) = is_a_theorem(equivalent(Y, X)).
% 290.33/37.33  Proof:
% 290.33/37.33    fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), Z)), true, equivalent(Y, X))
% 290.33/37.33  = { by axiom 3 (condensed_detachment) R->L }
% 290.33/37.33    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), Z), equivalent(Y, X))), true, equivalent(equivalent(X, equivalent(Y, Z)), Z), equivalent(Y, X))
% 290.33/37.33  = { by axiom 4 (pyo) }
% 290.33/37.33    fresh(true, true, equivalent(equivalent(X, equivalent(Y, Z)), Z), equivalent(Y, X))
% 290.33/37.33  = { by axiom 2 (condensed_detachment) }
% 290.33/37.33    is_a_theorem(equivalent(Y, X))
% 290.33/37.33  
% 290.33/37.33  Lemma 6: is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, equivalent(X, equivalent(Z, Y)))))) = true.
% 290.33/37.33  Proof:
% 290.33/37.33    is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, equivalent(X, equivalent(Z, Y))))))
% 290.33/37.33  = { by lemma 5 R->L }
% 290.33/37.33    fresh2(is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(Z, equivalent(X, equivalent(Z, Y)))), equivalent(X, equivalent(Z, Y))), equivalent(Z, Y))), true, equivalent(X, equivalent(Y, equivalent(Z, equivalent(X, equivalent(Z, Y))))))
% 290.33/37.33  = { by axiom 4 (pyo) }
% 290.33/37.33    fresh2(true, true, equivalent(X, equivalent(Y, equivalent(Z, equivalent(X, equivalent(Z, Y))))))
% 290.33/37.33  = { by axiom 1 (condensed_detachment) }
% 290.33/37.33    true
% 290.33/37.33  
% 290.33/37.33  Lemma 7: fresh2(is_a_theorem(X), true, equivalent(Y, equivalent(Z, equivalent(X, equivalent(Z, Y))))) = is_a_theorem(equivalent(Y, equivalent(Z, equivalent(X, equivalent(Z, Y))))).
% 290.33/37.33  Proof:
% 290.33/37.33    fresh2(is_a_theorem(X), true, equivalent(Y, equivalent(Z, equivalent(X, equivalent(Z, Y)))))
% 290.33/37.33  = { by axiom 3 (condensed_detachment) R->L }
% 290.33/37.33    fresh(is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, equivalent(X, equivalent(Z, Y)))))), true, X, equivalent(Y, equivalent(Z, equivalent(X, equivalent(Z, Y)))))
% 290.33/37.33  = { by lemma 6 }
% 290.33/37.33    fresh(true, true, X, equivalent(Y, equivalent(Z, equivalent(X, equivalent(Z, Y)))))
% 290.33/37.33  = { by axiom 2 (condensed_detachment) }
% 290.33/37.33    is_a_theorem(equivalent(Y, equivalent(Z, equivalent(X, equivalent(Z, Y)))))
% 290.33/37.33  
% 290.33/37.33  Lemma 8: fresh2(is_a_theorem(X), true, equivalent(Y, equivalent(equivalent(equivalent(equivalent(Z, equivalent(W, V)), V), equivalent(W, Z)), equivalent(Y, X)))) = is_a_theorem(equivalent(Y, equivalent(equivalent(equivalent(equivalent(Z, equivalent(W, V)), V), equivalent(W, Z)), equivalent(Y, X)))).
% 290.33/37.33  Proof:
% 290.33/37.33    fresh2(is_a_theorem(X), true, equivalent(Y, equivalent(equivalent(equivalent(equivalent(Z, equivalent(W, V)), V), equivalent(W, Z)), equivalent(Y, X))))
% 290.33/37.33  = { by axiom 3 (condensed_detachment) R->L }
% 290.33/37.33    fresh(is_a_theorem(equivalent(X, equivalent(Y, equivalent(equivalent(equivalent(equivalent(Z, equivalent(W, V)), V), equivalent(W, Z)), equivalent(Y, X))))), true, X, equivalent(Y, equivalent(equivalent(equivalent(equivalent(Z, equivalent(W, V)), V), equivalent(W, Z)), equivalent(Y, X))))
% 290.33/37.33  = { by lemma 7 R->L }
% 290.33/37.33    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(W, V)), V), equivalent(W, Z))), true, equivalent(X, equivalent(Y, equivalent(equivalent(equivalent(equivalent(Z, equivalent(W, V)), V), equivalent(W, Z)), equivalent(Y, X))))), true, X, equivalent(Y, equivalent(equivalent(equivalent(equivalent(Z, equivalent(W, V)), V), equivalent(W, Z)), equivalent(Y, X))))
% 290.33/37.33  = { by axiom 4 (pyo) }
% 290.33/37.33    fresh(fresh2(true, true, equivalent(X, equivalent(Y, equivalent(equivalent(equivalent(equivalent(Z, equivalent(W, V)), V), equivalent(W, Z)), equivalent(Y, X))))), true, X, equivalent(Y, equivalent(equivalent(equivalent(equivalent(Z, equivalent(W, V)), V), equivalent(W, Z)), equivalent(Y, X))))
% 290.33/37.33  = { by axiom 1 (condensed_detachment) }
% 290.33/37.33    fresh(true, true, X, equivalent(Y, equivalent(equivalent(equivalent(equivalent(Z, equivalent(W, V)), V), equivalent(W, Z)), equivalent(Y, X))))
% 290.33/37.33  = { by axiom 2 (condensed_detachment) }
% 290.33/37.33    is_a_theorem(equivalent(Y, equivalent(equivalent(equivalent(equivalent(Z, equivalent(W, V)), V), equivalent(W, Z)), equivalent(Y, X))))
% 290.33/37.33  
% 290.33/37.33  Lemma 9: is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, equivalent(Z, W)), W), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)))))) = true.
% 290.33/37.33  Proof:
% 290.33/37.33    is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, equivalent(Z, W)), W), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V))))))
% 290.33/37.33  = { by lemma 8 R->L }
% 290.33/37.33    fresh2(is_a_theorem(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V))), true, equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, equivalent(Z, W)), W), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V))))))
% 290.33/37.33  = { by axiom 4 (pyo) }
% 290.33/37.33    fresh2(true, true, equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, equivalent(Z, W)), W), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V))))))
% 290.33/37.33  = { by axiom 1 (condensed_detachment) }
% 290.33/37.33    true
% 290.33/37.33  
% 290.33/37.33  Lemma 10: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W))), true, W) = is_a_theorem(W).
% 290.33/37.33  Proof:
% 290.33/37.33    fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W))), true, W)
% 290.33/37.33  = { by axiom 3 (condensed_detachment) R->L }
% 290.33/37.33    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.33  = { by axiom 2 (condensed_detachment) R->L }
% 290.33/37.33    fresh(fresh(true, true, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.33  = { by axiom 1 (condensed_detachment) R->L }
% 290.33/37.33    fresh(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W))), true, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.33  = { by axiom 1 (condensed_detachment) R->L }
% 290.33/37.33    fresh(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), true, equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W))), true, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.33  = { by axiom 4 (pyo) R->L }
% 290.33/37.33    fresh(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(S, equivalent(X2, Y2)), Y2), equivalent(X2, S))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), true, equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W))), true, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.33  = { by axiom 3 (condensed_detachment) R->L }
% 290.33/37.33    fresh(fresh(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, equivalent(X2, Y2)), Y2), equivalent(X2, S)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y)))))), true, equivalent(equivalent(equivalent(S, equivalent(X2, Y2)), Y2), equivalent(X2, S)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), true, equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W))), true, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.33  = { by axiom 2 (condensed_detachment) R->L }
% 290.33/37.34    fresh(fresh(fresh2(fresh(fresh(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(S, equivalent(X2, Y2)), Y2), equivalent(X2, S)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y)))))), true, equivalent(equivalent(equivalent(S, equivalent(X2, Y2)), Y2), equivalent(X2, S)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), true, equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W))), true, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.34  = { by lemma 9 R->L }
% 290.33/37.34    fresh(fresh(fresh2(fresh(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(S, equivalent(X2, Y2)), Y2), equivalent(X2, S)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(S, equivalent(X2, Y2)), Y2), equivalent(X2, S)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y)))))), true, equivalent(equivalent(equivalent(S, equivalent(X2, Y2)), Y2), equivalent(X2, S)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), true, equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W))), true, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.34  = { by axiom 3 (condensed_detachment) }
% 290.33/37.34    fresh(fresh(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y)))))), true, equivalent(equivalent(equivalent(equivalent(S, equivalent(X2, Y2)), Y2), equivalent(X2, S)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y)))))), true, equivalent(equivalent(equivalent(S, equivalent(X2, Y2)), Y2), equivalent(X2, S)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), true, equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W))), true, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.34  = { by lemma 9 }
% 290.33/37.34    fresh(fresh(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(S, equivalent(X2, Y2)), Y2), equivalent(X2, S)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y)))))), true, equivalent(equivalent(equivalent(S, equivalent(X2, Y2)), Y2), equivalent(X2, S)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), true, equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W))), true, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.34  = { by axiom 1 (condensed_detachment) }
% 290.33/37.34    fresh(fresh(fresh2(fresh(true, true, equivalent(equivalent(equivalent(S, equivalent(X2, Y2)), Y2), equivalent(X2, S)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), true, equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W))), true, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.34  = { by axiom 2 (condensed_detachment) }
% 290.33/37.34    fresh(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), equivalent(X, Y))))), true, equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W))), true, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.34  = { by lemma 5 }
% 290.33/37.34    fresh(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W))), true, equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.34  = { by axiom 3 (condensed_detachment) }
% 290.33/37.34    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(V, equivalent(U, T)), T), equivalent(U, V))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.34  = { by axiom 4 (pyo) }
% 290.33/37.34    fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.34  = { by axiom 1 (condensed_detachment) }
% 290.33/37.34    fresh(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Y, equivalent(X, Z)), Z), W)), W)
% 290.33/37.34  = { by axiom 2 (condensed_detachment) }
% 290.33/37.34    is_a_theorem(W)
% 290.33/37.34  
% 290.33/37.34  Lemma 11: is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y)) = true.
% 290.33/37.34  Proof:
% 290.33/37.34    is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y))
% 290.33/37.34  = { by lemma 5 R->L }
% 290.33/37.34    fresh2(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), true, equivalent(equivalent(X, equivalent(X, Y)), Y))
% 290.33/37.34  = { by lemma 10 R->L }
% 290.33/37.34    fresh2(fresh2(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y)))))), equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))), equivalent(X, equivalent(X, equivalent(X, Y)))), equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))))), true, equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), true, equivalent(equivalent(X, equivalent(X, Y)), Y))
% 290.33/37.34  = { by lemma 8 R->L }
% 290.33/37.34    fresh2(fresh2(fresh2(is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y)))))), true, equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y)))))), equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))), equivalent(X, equivalent(X, equivalent(X, Y)))), equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))))), true, equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), true, equivalent(equivalent(X, equivalent(X, Y)), Y))
% 290.33/37.34  = { by lemma 6 }
% 290.33/37.34    fresh2(fresh2(fresh2(true, true, equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y)))))), equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))), equivalent(X, equivalent(X, equivalent(X, Y)))), equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))))), true, equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), true, equivalent(equivalent(X, equivalent(X, Y)), Y))
% 290.33/37.34  = { by axiom 1 (condensed_detachment) }
% 290.33/37.34    fresh2(fresh2(true, true, equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), equivalent(X, equivalent(Y, equivalent(X, equivalent(X, equivalent(X, Y))))))), true, equivalent(equivalent(X, equivalent(X, Y)), Y))
% 290.33/37.34  = { by axiom 1 (condensed_detachment) }
% 290.33/37.34    fresh2(true, true, equivalent(equivalent(X, equivalent(X, Y)), Y))
% 290.33/37.34  = { by axiom 1 (condensed_detachment) }
% 290.33/37.34    true
% 290.33/37.34  
% 290.33/37.34  Lemma 12: fresh2(is_a_theorem(equivalent(X, equivalent(X, Y))), true, Y) = is_a_theorem(Y).
% 290.33/37.34  Proof:
% 290.33/37.34    fresh2(is_a_theorem(equivalent(X, equivalent(X, Y))), true, Y)
% 290.33/37.34  = { by axiom 3 (condensed_detachment) R->L }
% 290.33/37.34    fresh(is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(X, equivalent(X, Y)), Y)
% 290.33/37.34  = { by lemma 11 }
% 290.33/37.34    fresh(true, true, equivalent(X, equivalent(X, Y)), Y)
% 290.33/37.34  = { by axiom 2 (condensed_detachment) }
% 290.33/37.34    is_a_theorem(Y)
% 290.33/37.34  
% 290.33/37.34  Lemma 13: fresh2(is_a_theorem(X), true, equivalent(X, equivalent(Y, Y))) = is_a_theorem(equivalent(X, equivalent(Y, Y))).
% 290.33/37.34  Proof:
% 290.33/37.34    fresh2(is_a_theorem(X), true, equivalent(X, equivalent(Y, Y)))
% 290.33/37.34  = { by axiom 3 (condensed_detachment) R->L }
% 290.33/37.34    fresh(is_a_theorem(equivalent(X, equivalent(X, equivalent(Y, Y)))), true, X, equivalent(X, equivalent(Y, Y)))
% 290.33/37.34  = { by lemma 5 R->L }
% 290.33/37.34    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y))), equivalent(Y, Y))), true, equivalent(X, equivalent(X, equivalent(Y, Y)))), true, X, equivalent(X, equivalent(Y, Y)))
% 290.33/37.34  = { by lemma 12 R->L }
% 290.33/37.34    fresh(fresh2(fresh2(is_a_theorem(equivalent(Y, equivalent(Y, equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y))), equivalent(Y, Y))))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y))), equivalent(Y, Y))), true, equivalent(X, equivalent(X, equivalent(Y, Y)))), true, X, equivalent(X, equivalent(Y, Y)))
% 290.33/37.34  = { by lemma 7 R->L }
% 290.33/37.34    fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y)))), true, equivalent(Y, equivalent(Y, equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y))), equivalent(Y, Y))))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y))), equivalent(Y, Y))), true, equivalent(X, equivalent(X, equivalent(Y, Y)))), true, X, equivalent(X, equivalent(Y, Y)))
% 290.33/37.35  = { by lemma 5 R->L }
% 290.33/37.35    fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(equivalent(X, equivalent(Y, Y)), Z)), Z)), true, equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y)))), true, equivalent(Y, equivalent(Y, equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y))), equivalent(Y, Y))))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y))), equivalent(Y, Y))), true, equivalent(X, equivalent(X, equivalent(Y, Y)))), true, X, equivalent(X, equivalent(Y, Y)))
% 290.33/37.35  = { by lemma 11 }
% 290.33/37.35    fresh(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y)))), true, equivalent(Y, equivalent(Y, equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y))), equivalent(Y, Y))))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y))), equivalent(Y, Y))), true, equivalent(X, equivalent(X, equivalent(Y, Y)))), true, X, equivalent(X, equivalent(Y, Y)))
% 290.33/37.35  = { by axiom 1 (condensed_detachment) }
% 290.33/37.35    fresh(fresh2(fresh2(fresh2(true, true, equivalent(Y, equivalent(Y, equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y))), equivalent(Y, Y))))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y))), equivalent(Y, Y))), true, equivalent(X, equivalent(X, equivalent(Y, Y)))), true, X, equivalent(X, equivalent(Y, Y)))
% 290.33/37.35  = { by axiom 1 (condensed_detachment) }
% 290.33/37.35    fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(X, equivalent(Y, Y))), equivalent(Y, Y))), true, equivalent(X, equivalent(X, equivalent(Y, Y)))), true, X, equivalent(X, equivalent(Y, Y)))
% 290.33/37.35  = { by axiom 1 (condensed_detachment) }
% 290.33/37.35    fresh(fresh2(true, true, equivalent(X, equivalent(X, equivalent(Y, Y)))), true, X, equivalent(X, equivalent(Y, Y)))
% 290.33/37.35  = { by axiom 1 (condensed_detachment) }
% 290.33/37.35    fresh(true, true, X, equivalent(X, equivalent(Y, Y)))
% 290.33/37.35  = { by axiom 2 (condensed_detachment) }
% 290.33/37.35    is_a_theorem(equivalent(X, equivalent(Y, Y)))
% 290.33/37.35  
% 290.33/37.35  Lemma 14: fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z))), true, Z) = is_a_theorem(Z).
% 290.33/37.35  Proof:
% 290.33/37.35    fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z))), true, Z)
% 290.33/37.35  = { by axiom 3 (condensed_detachment) R->L }
% 290.33/37.35    fresh(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)
% 290.33/37.35  = { by lemma 10 R->L }
% 290.33/37.35    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(Y, X)), X), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)))), true, equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)
% 290.33/37.35  = { by lemma 12 R->L }
% 290.33/37.35    fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(equivalent(Y, equivalent(Y, X)), X), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)))))), true, equivalent(equivalent(equivalent(Y, equivalent(Y, X)), X), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)))), true, equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)
% 290.33/37.35  = { by lemma 7 R->L }
% 290.33/37.35    fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(Y, equivalent(Y, X)), X)), true, equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(equivalent(Y, equivalent(Y, X)), X), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)))))), true, equivalent(equivalent(equivalent(Y, equivalent(Y, X)), X), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)))), true, equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)
% 290.33/37.35  = { by lemma 11 }
% 290.33/37.35    fresh(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(equivalent(Y, equivalent(Y, X)), X), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)))))), true, equivalent(equivalent(equivalent(Y, equivalent(Y, X)), X), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)))), true, equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)
% 290.33/37.35  = { by axiom 1 (condensed_detachment) }
% 290.33/37.35    fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(Y, equivalent(Y, X)), X), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z), equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)))), true, equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)
% 290.33/37.35  = { by axiom 1 (condensed_detachment) }
% 290.33/37.35    fresh(fresh2(true, true, equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)
% 290.33/37.35  = { by axiom 1 (condensed_detachment) }
% 290.33/37.35    fresh(true, true, equivalent(X, equivalent(equivalent(Y, equivalent(Y, X)), Z)), Z)
% 290.33/37.35  = { by axiom 2 (condensed_detachment) }
% 290.33/37.35    is_a_theorem(Z)
% 290.33/37.35  
% 290.33/37.35  Lemma 15: is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, equivalent(Z, equivalent(Z, Y)))))) = true.
% 290.33/37.35  Proof:
% 290.33/37.35    is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, equivalent(Z, equivalent(Z, Y))))))
% 290.33/37.35  = { by lemma 14 R->L }
% 290.33/37.35    fresh2(is_a_theorem(equivalent(Y, equivalent(equivalent(Z, equivalent(Z, Y)), equivalent(X, equivalent(Y, equivalent(X, equivalent(Z, equivalent(Z, Y)))))))), true, equivalent(X, equivalent(Y, equivalent(X, equivalent(Z, equivalent(Z, Y))))))
% 290.33/37.35  = { by lemma 6 }
% 290.33/37.35    fresh2(true, true, equivalent(X, equivalent(Y, equivalent(X, equivalent(Z, equivalent(Z, Y))))))
% 290.33/37.35  = { by axiom 1 (condensed_detachment) }
% 290.33/37.35    true
% 290.33/37.35  
% 290.33/37.35  Lemma 16: is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))))) = true.
% 290.33/37.35  Proof:
% 290.33/37.35    is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.35  = { by lemma 5 R->L }
% 290.33/37.35    fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.35  = { by lemma 10 R->L }
% 290.33/37.35    fresh2(fresh2(is_a_theorem(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.35  = { by axiom 2 (condensed_detachment) R->L }
% 290.33/37.35    fresh2(fresh2(fresh(true, true, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.35  = { by axiom 1 (condensed_detachment) R->L }
% 290.33/37.35    fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), true, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.35  = { by axiom 1 (condensed_detachment) R->L }
% 290.33/37.35    fresh2(fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(Y, equivalent(Z, equivalent(Y, Z))), equivalent(equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))))), true, equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), true, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.36  = { by axiom 1 (condensed_detachment) R->L }
% 290.33/37.36    fresh2(fresh2(fresh(fresh2(fresh2(fresh2(true, true, equivalent(Y, equivalent(Z, equivalent(Y, Z)))), true, equivalent(equivalent(Y, equivalent(Z, equivalent(Y, Z))), equivalent(equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))))), true, equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), true, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.36  = { by lemma 6 R->L }
% 290.33/37.36    fresh2(fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(Z, equivalent(Z, equivalent(Y, equivalent(Z, equivalent(Y, Z)))))), true, equivalent(Y, equivalent(Z, equivalent(Y, Z)))), true, equivalent(equivalent(Y, equivalent(Z, equivalent(Y, Z))), equivalent(equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))))), true, equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), true, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.36  = { by lemma 12 }
% 290.33/37.36    fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(Y, equivalent(Z, equivalent(Y, Z)))), true, equivalent(equivalent(Y, equivalent(Z, equivalent(Y, Z))), equivalent(equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))))), true, equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), true, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.36  = { by lemma 13 }
% 290.33/37.36    fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(Y, equivalent(Z, equivalent(Y, Z))), equivalent(equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))))), true, equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), true, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.36  = { by lemma 10 }
% 290.33/37.36    fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), true, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y))))), equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.36  = { by axiom 3 (condensed_detachment) }
% 290.33/37.36    fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(Y, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))))), true, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.36  = { by lemma 15 }
% 290.33/37.36    fresh2(fresh2(fresh2(true, true, equivalent(equivalent(Z, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.36  = { by axiom 1 (condensed_detachment) }
% 290.33/37.36    fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y))), equivalent(X, Y)), Y)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.36  = { by axiom 1 (condensed_detachment) }
% 290.33/37.36    fresh2(true, true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Z, equivalent(X, Y)))))
% 290.33/37.36  = { by axiom 1 (condensed_detachment) }
% 290.33/37.36    true
% 290.33/37.36  
% 290.33/37.36  Lemma 17: fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(Y, X)) = is_a_theorem(equivalent(Y, X)).
% 290.33/37.36  Proof:
% 290.33/37.36    fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(Y, X))
% 290.33/37.36  = { by axiom 3 (condensed_detachment) R->L }
% 290.33/37.36    fresh(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 290.33/37.36  = { by lemma 14 R->L }
% 290.33/37.36    fresh(fresh2(is_a_theorem(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(equivalent(X, Y), equivalent(Y, X))))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 290.33/37.36  = { by lemma 16 }
% 290.33/37.36    fresh(fresh2(true, true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 290.33/37.36  = { by axiom 1 (condensed_detachment) }
% 290.33/37.36    fresh(true, true, equivalent(X, Y), equivalent(Y, X))
% 290.33/37.36  = { by axiom 2 (condensed_detachment) }
% 290.33/37.36    is_a_theorem(equivalent(Y, X))
% 290.33/37.36  
% 290.33/37.36  Lemma 18: is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))))) = true.
% 290.33/37.36  Proof:
% 290.33/37.36    is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z)))))
% 290.33/37.36  = { by lemma 5 R->L }
% 290.33/37.36    fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z)))))
% 290.33/37.36  = { by lemma 10 R->L }
% 290.33/37.36    fresh2(fresh2(is_a_theorem(equivalent(equivalent(Y, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z)))))
% 290.33/37.36  = { by lemma 14 R->L }
% 290.33/37.36    fresh2(fresh2(fresh2(is_a_theorem(equivalent(Z, equivalent(equivalent(Y, equivalent(Y, Z)), equivalent(equivalent(Y, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)))))), true, equivalent(equivalent(Y, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z)))))
% 290.33/37.37  = { by lemma 14 R->L }
% 290.33/37.37    fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(Z, equivalent(equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)), equivalent(Z, equivalent(equivalent(Y, equivalent(Y, Z)), equivalent(equivalent(Y, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)))))))), true, equivalent(Z, equivalent(equivalent(Y, equivalent(Y, Z)), equivalent(equivalent(Y, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)))))), true, equivalent(equivalent(Y, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z)))))
% 290.33/37.37  = { by lemma 15 }
% 290.33/37.37    fresh2(fresh2(fresh2(fresh2(true, true, equivalent(Z, equivalent(equivalent(Y, equivalent(Y, Z)), equivalent(equivalent(Y, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)))))), true, equivalent(equivalent(Y, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z)))))
% 290.33/37.37  = { by axiom 1 (condensed_detachment) }
% 290.33/37.37    fresh2(fresh2(fresh2(true, true, equivalent(equivalent(Y, equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)))), true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z)))))
% 290.33/37.37  = { by axiom 1 (condensed_detachment) }
% 290.33/37.37    fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z))), equivalent(X, Z)), Z)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z)))))
% 290.33/37.37  = { by axiom 1 (condensed_detachment) }
% 290.33/37.37    fresh2(true, true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Y, equivalent(X, Z)))))
% 290.33/37.37  = { by axiom 1 (condensed_detachment) }
% 290.33/37.37    true
% 290.33/37.37  
% 290.33/37.37  Goal 1 (prove_yro): is_a_theorem(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))) = true.
% 290.33/37.37  Proof:
% 290.33/37.37    is_a_theorem(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.37  = { by lemma 10 R->L }
% 290.33/37.37    fresh2(is_a_theorem(equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.37  = { by lemma 17 R->L }
% 290.33/37.37    fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.38  = { by lemma 10 R->L }
% 290.33/37.38    fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.38  = { by lemma 13 R->L }
% 290.33/37.38    fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.38  = { by axiom 2 (condensed_detachment) R->L }
% 290.33/37.38    fresh2(fresh2(fresh2(fresh2(fresh(true, true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.38  = { by axiom 1 (condensed_detachment) R->L }
% 290.33/37.38    fresh2(fresh2(fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.38  = { by axiom 1 (condensed_detachment) R->L }
% 290.33/37.38    fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(true, true, equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.38  = { by lemma 16 R->L }
% 290.33/37.38    fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, b), a), equivalent(equivalent(equivalent(c, b), a), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)))))), true, equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.39  = { by lemma 12 }
% 290.33/37.39    fresh2(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.39  = { by axiom 3 (condensed_detachment) R->L }
% 290.33/37.39    fresh2(fresh2(fresh2(fresh2(fresh(fresh(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))))), true, equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.39  = { by lemma 12 R->L }
% 290.33/37.39    fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))))), true, equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.39  = { by lemma 18 }
% 290.33/37.39    fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(true, true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))))), true, equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.39  = { by axiom 1 (condensed_detachment) }
% 290.33/37.39    fresh2(fresh2(fresh2(fresh2(fresh(fresh(true, true, equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.39  = { by axiom 2 (condensed_detachment) }
% 290.33/37.39    fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.39  = { by axiom 3 (condensed_detachment) }
% 290.33/37.39    fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.40  = { by lemma 17 R->L }
% 290.33/37.40    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.40  = { by lemma 10 R->L }
% 290.33/37.40    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.40  = { by lemma 17 R->L }
% 290.33/37.40    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.40  = { by lemma 10 R->L }
% 290.33/37.40    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.41  = { by lemma 13 R->L }
% 290.33/37.41    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.41  = { by lemma 10 R->L }
% 290.33/37.41    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b))))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.41  = { by lemma 18 }
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% 290.33/37.42  = { by axiom 1 (condensed_detachment) }
% 290.33/37.42    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.42  = { by axiom 1 (condensed_detachment) }
% 290.33/37.42    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.42  = { by axiom 1 (condensed_detachment) }
% 290.33/37.42    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), equivalent(a, b)), b), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.42  = { by axiom 1 (condensed_detachment) }
% 290.33/37.42    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.42  = { by axiom 1 (condensed_detachment) }
% 290.33/37.42    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(a, equivalent(equivalent(equivalent(c, b), a), equivalent(c, b))), equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.42  = { by axiom 1 (condensed_detachment) }
% 290.33/37.42    fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.42  = { by axiom 1 (condensed_detachment) }
% 290.33/37.42    fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.42  = { by axiom 1 (condensed_detachment) }
% 290.33/37.42    fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))), equivalent(c, equivalent(equivalent(c, b), a)))), true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.42  = { by axiom 1 (condensed_detachment) }
% 290.33/37.42    fresh2(fresh2(true, true, equivalent(equivalent(c, equivalent(equivalent(c, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), a), equivalent(c, b)), b), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a)))))), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.42  = { by axiom 1 (condensed_detachment) }
% 290.33/37.42    fresh2(true, true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(c, b), a))))
% 290.33/37.42  = { by axiom 1 (condensed_detachment) }
% 290.33/37.42    true
% 290.33/37.42  % SZS output end Proof
% 290.33/37.42  
% 290.33/37.42  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------