%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL127-1 : 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 : n011.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 08:17:34 EDT 2023

% Result   : Unsatisfiable 254.63s 32.70s
% Output   : Proof 256.98s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL127-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34  % Computer : n011.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug 24 21:00:52 EDT 2023
% 0.21/0.34  % CPUTime  : 
% 254.63/32.70  Command-line arguments: --no-flatten-goal
% 254.63/32.70  
% 254.63/32.70  % SZS status Unsatisfiable
% 254.63/32.70  
% 255.32/32.77  % SZS output start Proof
% 255.32/32.77  Take the following subset of the input axioms:
% 255.32/32.77    fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 255.32/32.77    fof(prove_lg_2, negated_conjecture, ~is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))).
% 255.32/32.77    fof(s_2, axiom, ![Z, U, X2, Y2]: is_a_theorem(equivalent(equivalent(X2, equivalent(Y2, Z)), equivalent(X2, equivalent(equivalent(Y2, U), equivalent(Z, U)))))).
% 255.32/32.77  
% 255.32/32.77  Now clausify the problem and encode Horn clauses using encoding 3 of
% 255.32/32.77  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 255.32/32.77  We repeatedly replace C & s=t => u=v by the two clauses:
% 255.32/32.77    fresh(y, y, x1...xn) = u
% 255.32/32.77    C => fresh(s, t, x1...xn) = v
% 255.32/32.77  where fresh is a fresh function symbol and x1..xn are the free
% 255.32/32.77  variables of u and v.
% 255.32/32.77  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 255.32/32.77  input problem has no model of domain size 1).
% 255.32/32.77  
% 255.32/32.77  The encoding turns the above axioms into the following unit equations and goals:
% 255.32/32.77  
% 255.32/32.77  Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 255.32/32.77  Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 255.32/32.77  Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 255.32/32.77  Axiom 4 (s_2): is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(equivalent(Y, W), equivalent(Z, W))))) = true.
% 255.32/32.77  
% 255.32/32.77  Lemma 5: fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(X, equivalent(equivalent(Y, W), equivalent(Z, W)))) = is_a_theorem(equivalent(X, equivalent(equivalent(Y, W), equivalent(Z, W)))).
% 255.32/32.77  Proof:
% 255.32/32.77    fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(X, equivalent(equivalent(Y, W), equivalent(Z, W))))
% 255.32/32.77  = { by axiom 3 (condensed_detachment) R->L }
% 255.32/32.77    fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(equivalent(Y, W), equivalent(Z, W))))), true, equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(equivalent(Y, W), equivalent(Z, W))))
% 255.32/32.77  = { by axiom 4 (s_2) }
% 255.32/32.77    fresh(true, true, equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(equivalent(Y, W), equivalent(Z, W))))
% 255.32/32.77  = { by axiom 2 (condensed_detachment) }
% 255.32/32.77    is_a_theorem(equivalent(X, equivalent(equivalent(Y, W), equivalent(Z, W))))
% 255.32/32.77  
% 255.32/32.77  Lemma 6: is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, W), equivalent(equivalent(equivalent(Y, V), equivalent(Z, V)), W)))) = true.
% 255.32/32.77  Proof:
% 255.32/32.77    is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, W), equivalent(equivalent(equivalent(Y, V), equivalent(Z, V)), W))))
% 255.32/32.77  = { by lemma 5 R->L }
% 255.32/32.77    fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(equivalent(Y, V), equivalent(Z, V))))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, W), equivalent(equivalent(equivalent(Y, V), equivalent(Z, V)), W))))
% 255.32/32.77  = { by axiom 4 (s_2) }
% 255.32/32.77    fresh2(true, true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, W), equivalent(equivalent(equivalent(Y, V), equivalent(Z, V)), W))))
% 255.32/32.77  = { by axiom 1 (condensed_detachment) }
% 255.32/32.77    true
% 255.32/32.77  
% 255.32/32.77  Lemma 7: fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(equivalent(X, W), equivalent(equivalent(equivalent(Y, V), equivalent(Z, V)), W))) = is_a_theorem(equivalent(equivalent(X, W), equivalent(equivalent(equivalent(Y, V), equivalent(Z, V)), W))).
% 255.32/32.77  Proof:
% 255.32/32.77    fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(equivalent(X, W), equivalent(equivalent(equivalent(Y, V), equivalent(Z, V)), W)))
% 255.32/32.77  = { by axiom 3 (condensed_detachment) R->L }
% 255.32/32.77    fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, W), equivalent(equivalent(equivalent(Y, V), equivalent(Z, V)), W)))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, W), equivalent(equivalent(equivalent(Y, V), equivalent(Z, V)), W)))
% 255.32/32.77  = { by lemma 6 }
% 255.32/32.77    fresh(true, true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, W), equivalent(equivalent(equivalent(Y, V), equivalent(Z, V)), W)))
% 255.32/32.77  = { by axiom 2 (condensed_detachment) }
% 255.32/32.77    is_a_theorem(equivalent(equivalent(X, W), equivalent(equivalent(equivalent(Y, V), equivalent(Z, V)), W)))
% 255.32/32.77  
% 255.32/32.77  Lemma 8: fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), W)), true, equivalent(equivalent(equivalent(X, V), equivalent(equivalent(equivalent(Y, U), equivalent(Z, U)), V)), W)) = is_a_theorem(equivalent(equivalent(equivalent(X, V), equivalent(equivalent(equivalent(Y, U), equivalent(Z, U)), V)), W)).
% 255.32/32.77  Proof:
% 255.32/32.77    fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), W)), true, equivalent(equivalent(equivalent(X, V), equivalent(equivalent(equivalent(Y, U), equivalent(Z, U)), V)), W))
% 255.32/32.77  = { by axiom 3 (condensed_detachment) R->L }
% 255.32/32.77    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), W), equivalent(equivalent(equivalent(X, V), equivalent(equivalent(equivalent(Y, U), equivalent(Z, U)), V)), W))), true, equivalent(equivalent(X, equivalent(Y, Z)), W), equivalent(equivalent(equivalent(X, V), equivalent(equivalent(equivalent(Y, U), equivalent(Z, U)), V)), W))
% 255.32/32.77  = { by lemma 7 R->L }
% 255.32/32.77    fresh(fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(equivalent(Y, U), equivalent(Z, U))))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), W), equivalent(equivalent(equivalent(X, V), equivalent(equivalent(equivalent(Y, U), equivalent(Z, U)), V)), W))), true, equivalent(equivalent(X, equivalent(Y, Z)), W), equivalent(equivalent(equivalent(X, V), equivalent(equivalent(equivalent(Y, U), equivalent(Z, U)), V)), W))
% 255.32/32.77  = { by axiom 4 (s_2) }
% 255.32/32.77    fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), W), equivalent(equivalent(equivalent(X, V), equivalent(equivalent(equivalent(Y, U), equivalent(Z, U)), V)), W))), true, equivalent(equivalent(X, equivalent(Y, Z)), W), equivalent(equivalent(equivalent(X, V), equivalent(equivalent(equivalent(Y, U), equivalent(Z, U)), V)), W))
% 255.32/32.77  = { by axiom 1 (condensed_detachment) }
% 255.32/32.77    fresh(true, true, equivalent(equivalent(X, equivalent(Y, Z)), W), equivalent(equivalent(equivalent(X, V), equivalent(equivalent(equivalent(Y, U), equivalent(Z, U)), V)), W))
% 255.32/32.77  = { by axiom 2 (condensed_detachment) }
% 255.32/32.77    is_a_theorem(equivalent(equivalent(equivalent(X, V), equivalent(equivalent(equivalent(Y, U), equivalent(Z, U)), V)), W))
% 255.32/32.77  
% 255.32/32.77  Lemma 9: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(X, equivalent(equivalent(Z, U), equivalent(V, U))))) = true.
% 255.32/32.77  Proof:
% 255.32/32.77    is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(X, equivalent(equivalent(Z, U), equivalent(V, U)))))
% 255.32/32.77  = { by lemma 8 R->L }
% 255.32/32.77    fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Z, V)), equivalent(X, equivalent(equivalent(Z, U), equivalent(V, U))))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(X, equivalent(equivalent(Z, U), equivalent(V, U)))))
% 255.32/32.77  = { by axiom 4 (s_2) }
% 255.32/32.77    fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(X, equivalent(equivalent(Z, U), equivalent(V, U)))))
% 255.32/32.77  = { by axiom 1 (condensed_detachment) }
% 255.32/32.77    true
% 255.32/32.77  
% 255.32/32.77  Lemma 10: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y))), true, equivalent(X, equivalent(equivalent(Z, U), equivalent(V, U)))) = is_a_theorem(equivalent(X, equivalent(equivalent(Z, U), equivalent(V, U)))).
% 255.32/32.77  Proof:
% 255.32/32.77    fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y))), true, equivalent(X, equivalent(equivalent(Z, U), equivalent(V, U))))
% 255.32/32.77  = { by axiom 3 (condensed_detachment) R->L }
% 255.32/32.77    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(X, equivalent(equivalent(Z, U), equivalent(V, U))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(X, equivalent(equivalent(Z, U), equivalent(V, U))))
% 255.32/32.77  = { by lemma 9 }
% 255.32/32.77    fresh(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(X, equivalent(equivalent(Z, U), equivalent(V, U))))
% 255.32/32.77  = { by axiom 2 (condensed_detachment) }
% 255.32/32.77    is_a_theorem(equivalent(X, equivalent(equivalent(Z, U), equivalent(V, U))))
% 255.32/32.77  
% 255.32/32.77  Lemma 11: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(equivalent(X, U), equivalent(equivalent(equivalent(Z, T), equivalent(V, T)), U)))) = true.
% 255.32/32.77  Proof:
% 255.32/32.77    is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(equivalent(X, U), equivalent(equivalent(equivalent(Z, T), equivalent(V, T)), U))))
% 255.32/32.77  = { by lemma 8 R->L }
% 255.32/32.77    fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Z, V)), equivalent(equivalent(X, U), equivalent(equivalent(equivalent(Z, T), equivalent(V, T)), U)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(equivalent(X, U), equivalent(equivalent(equivalent(Z, T), equivalent(V, T)), U))))
% 255.32/32.77  = { by lemma 6 }
% 255.32/32.77    fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(equivalent(X, U), equivalent(equivalent(equivalent(Z, T), equivalent(V, T)), U))))
% 255.32/32.77  = { by axiom 1 (condensed_detachment) }
% 255.32/32.77    true
% 255.32/32.77  
% 255.32/32.77  Lemma 12: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W)))) = true.
% 255.32/32.77  Proof:
% 255.32/32.77    is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 255.32/32.77  = { by lemma 10 R->L }
% 255.32/32.77    fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(equivalent(V, U), equivalent(T, U)), equivalent(Z, Y))), equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(equivalent(V, U), equivalent(T, U)), equivalent(Z, Y))))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 255.32/32.77  = { by lemma 11 }
% 255.32/32.77    fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 255.32/32.77  = { by axiom 1 (condensed_detachment) }
% 255.32/32.77    true
% 255.32/32.77  
% 255.32/32.77  Lemma 13: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, Y))), true, equivalent(equivalent(X, W), equivalent(Z, W))) = is_a_theorem(equivalent(equivalent(X, W), equivalent(Z, W))).
% 255.32/32.77  Proof:
% 255.32/32.77    fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, Y))), true, equivalent(equivalent(X, W), equivalent(Z, W)))
% 255.32/32.77  = { by axiom 3 (condensed_detachment) R->L }
% 255.32/32.77    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W)))), true, equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W)))
% 255.32/32.77  = { by lemma 12 }
% 255.32/32.77    fresh(true, true, equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W)))
% 255.32/32.77  = { by axiom 2 (condensed_detachment) }
% 255.32/32.77    is_a_theorem(equivalent(equivalent(X, W), equivalent(Z, W)))
% 255.32/32.77  
% 255.32/32.77  Lemma 14: is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(X, Y), Z))) = true.
% 255.32/32.77  Proof:
% 255.32/32.77    is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(X, Y), Z)))
% 255.32/32.77  = { by lemma 13 R->L }
% 255.32/32.77    fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(W, V), equivalent(U, V)), Y)), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(W, V), equivalent(U, V)), Y)))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(X, Y), Z)))
% 255.32/32.77  = { by lemma 11 }
% 255.32/32.77    fresh2(true, true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(X, Y), Z)))
% 255.32/32.77  = { by axiom 1 (condensed_detachment) }
% 255.32/32.77    true
% 255.32/32.77  
% 255.32/32.77  Lemma 15: fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), W)), true, equivalent(equivalent(equivalent(equivalent(X, Y), V), equivalent(Z, V)), W)) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), V), equivalent(Z, V)), W)).
% 255.32/32.77  Proof:
% 255.32/32.77    fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), W)), true, equivalent(equivalent(equivalent(equivalent(X, Y), V), equivalent(Z, V)), W))
% 255.32/32.77  = { by axiom 3 (condensed_detachment) R->L }
% 255.32/32.77    fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), W), equivalent(equivalent(equivalent(equivalent(X, Y), V), equivalent(Z, V)), W))), true, equivalent(equivalent(equivalent(X, Y), Z), W), equivalent(equivalent(equivalent(equivalent(X, Y), V), equivalent(Z, V)), W))
% 255.32/32.77  = { by lemma 7 R->L }
% 255.32/32.77    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(X, Y), Z))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), W), equivalent(equivalent(equivalent(equivalent(X, Y), V), equivalent(Z, V)), W))), true, equivalent(equivalent(equivalent(X, Y), Z), W), equivalent(equivalent(equivalent(equivalent(X, Y), V), equivalent(Z, V)), W))
% 255.32/32.77  = { by lemma 14 }
% 255.32/32.77    fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), W), equivalent(equivalent(equivalent(equivalent(X, Y), V), equivalent(Z, V)), W))), true, equivalent(equivalent(equivalent(X, Y), Z), W), equivalent(equivalent(equivalent(equivalent(X, Y), V), equivalent(Z, V)), W))
% 255.32/32.77  = { by axiom 1 (condensed_detachment) }
% 255.32/32.77    fresh(true, true, equivalent(equivalent(equivalent(X, Y), Z), W), equivalent(equivalent(equivalent(equivalent(X, Y), V), equivalent(Z, V)), W))
% 255.32/32.77  = { by axiom 2 (condensed_detachment) }
% 255.32/32.77    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), V), equivalent(Z, V)), W))
% 255.32/32.77  
% 255.32/32.77  Lemma 16: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z)), equivalent(equivalent(X, Y), W))) = true.
% 255.32/32.77  Proof:
% 255.32/32.77    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z)), equivalent(equivalent(X, Y), W)))
% 255.32/32.77  = { by lemma 15 R->L }
% 255.32/32.77    fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), W), equivalent(equivalent(X, Y), W))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z)), equivalent(equivalent(X, Y), W)))
% 255.32/32.77  = { by lemma 14 }
% 255.32/32.77    fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z)), equivalent(equivalent(X, Y), W)))
% 255.32/32.77  = { by axiom 1 (condensed_detachment) }
% 255.32/32.77    true
% 255.32/32.77  
% 255.32/32.77  Lemma 17: is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Y))) = true.
% 255.32/32.77  Proof:
% 255.32/32.77    is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Y)))
% 255.32/32.77  = { by axiom 2 (condensed_detachment) R->L }
% 255.32/32.78    fresh(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y))), equivalent(equivalent(X, Y), equivalent(X, Y)))
% 255.32/32.78  = { by lemma 16 R->L }
% 255.32/32.78    fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y))), equivalent(equivalent(X, Y), equivalent(X, Y)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y))), equivalent(equivalent(X, Y), equivalent(X, Y)))
% 255.32/32.78  = { by axiom 3 (condensed_detachment) }
% 255.32/32.78    fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), Y)))), true, equivalent(equivalent(X, Y), equivalent(X, Y)))
% 255.32/32.78  = { by lemma 11 }
% 255.32/32.78    fresh2(true, true, equivalent(equivalent(X, Y), equivalent(X, Y)))
% 255.32/32.78  = { by axiom 1 (condensed_detachment) }
% 255.32/32.78    true
% 255.32/32.78  
% 255.32/32.78  Lemma 18: is_a_theorem(equivalent(equivalent(X, equivalent(Y, Y)), X)) = true.
% 255.32/32.78  Proof:
% 255.32/32.78    is_a_theorem(equivalent(equivalent(X, equivalent(Y, Y)), X))
% 255.32/32.78  = { by axiom 2 (condensed_detachment) R->L }
% 255.32/32.78    fresh(true, true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))), equivalent(equivalent(X, equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y)))), equivalent(equivalent(X, equivalent(Y, Y)), X))
% 255.32/32.78  = { by axiom 1 (condensed_detachment) R->L }
% 255.32/32.78    fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))), equivalent(equivalent(X, equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y)))), equivalent(equivalent(X, equivalent(Y, Y)), X))), true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))), equivalent(equivalent(X, equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y)))), equivalent(equivalent(X, equivalent(Y, Y)), X))
% 255.32/32.78  = { by lemma 16 R->L }
% 255.32/32.78    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(Y, Y)), equivalent(X, equivalent(Y, Y))), equivalent(equivalent(X, equivalent(Y, Y)), X))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))), equivalent(equivalent(X, equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y)))), equivalent(equivalent(X, equivalent(Y, Y)), X))), true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))), equivalent(equivalent(X, equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y)))), equivalent(equivalent(X, equivalent(Y, Y)), X))
% 255.32/32.78  = { by lemma 15 }
% 255.32/32.78    fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))), equivalent(equivalent(X, equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y)))), equivalent(equivalent(X, equivalent(Y, Y)), X))), true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))), equivalent(equivalent(X, equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y)))), equivalent(equivalent(X, equivalent(Y, Y)), X))
% 255.32/32.78  = { by axiom 3 (condensed_detachment) }
% 255.32/32.78    fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))), equivalent(equivalent(X, equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))))), true, equivalent(equivalent(X, equivalent(Y, Y)), X))
% 255.32/32.78  = { by lemma 15 R->L }
% 255.32/32.78    fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(Z, Y)), equivalent(equivalent(X, equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))))), true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))), equivalent(equivalent(X, equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))))), true, equivalent(equivalent(X, equivalent(Y, Y)), X))
% 255.32/32.78  = { by axiom 4 (s_2) }
% 255.32/32.78    fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))), equivalent(equivalent(X, equivalent(Y, Y)), equivalent(equivalent(Z, Y), equivalent(Y, Y))))), true, equivalent(equivalent(X, equivalent(Y, Y)), X))
% 255.32/32.78  = { by axiom 1 (condensed_detachment) }
% 255.32/32.78    fresh2(true, true, equivalent(equivalent(X, equivalent(Y, Y)), X))
% 255.32/32.78  = { by axiom 1 (condensed_detachment) }
% 255.32/32.78    true
% 255.32/32.78  
% 255.32/32.78  Lemma 19: fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z)) = is_a_theorem(equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z)).
% 255.32/32.78  Proof:
% 255.32/32.78    fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 255.32/32.78  = { by axiom 3 (condensed_detachment) R->L }
% 255.32/32.78    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 255.32/32.78  = { by lemma 7 R->L }
% 255.32/32.78    fresh(fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Y))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 255.32/32.78  = { by lemma 17 }
% 255.32/32.78    fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 255.32/32.78  = { by axiom 1 (condensed_detachment) }
% 255.32/32.78    fresh(true, true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 255.32/32.78  = { by axiom 2 (condensed_detachment) }
% 255.32/32.78    is_a_theorem(equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 255.32/32.78  
% 255.32/32.78  Lemma 20: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, Z), Y)), X)) = true.
% 255.32/32.78  Proof:
% 255.32/32.78    is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, Z), Y)), X))
% 255.32/32.78  = { by lemma 19 R->L }
% 255.32/32.78    fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Z, Z)), X)), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, Z), Y)), X))
% 255.32/32.78  = { by lemma 18 }
% 255.32/32.78    fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, Z), Y)), X))
% 255.32/32.78  = { by axiom 1 (condensed_detachment) }
% 255.32/32.78    true
% 255.32/32.78  
% 255.32/32.78  Lemma 21: fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Y)), Z)), true, equivalent(X, Z)) = is_a_theorem(equivalent(X, Z)).
% 255.32/32.78  Proof:
% 255.32/32.78    fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Y)), Z)), true, equivalent(X, Z))
% 255.32/32.78  = { by axiom 3 (condensed_detachment) R->L }
% 255.32/32.78    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), Z), equivalent(X, Z))), true, equivalent(equivalent(X, equivalent(Y, Y)), Z), equivalent(X, Z))
% 255.32/32.78  = { by lemma 13 R->L }
% 255.32/32.78    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Y)), equivalent(Y, Y)), equivalent(X, equivalent(Y, Y)))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Y)), Z), equivalent(X, Z))), true, equivalent(equivalent(X, equivalent(Y, Y)), Z), equivalent(X, Z))
% 255.32/32.78  = { by lemma 18 }
% 255.32/32.78    fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, Y)), Z), equivalent(X, Z))), true, equivalent(equivalent(X, equivalent(Y, Y)), Z), equivalent(X, Z))
% 255.32/32.78  = { by axiom 1 (condensed_detachment) }
% 255.32/32.78    fresh(true, true, equivalent(equivalent(X, equivalent(Y, Y)), Z), equivalent(X, Z))
% 255.32/32.78  = { by axiom 2 (condensed_detachment) }
% 255.32/32.78    is_a_theorem(equivalent(X, Z))
% 255.32/32.78  
% 255.32/32.78  Lemma 22: is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W)))) = true.
% 255.32/32.78  Proof:
% 255.32/32.78    is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W))))
% 255.32/32.78  = { by lemma 21 R->L }
% 255.32/32.78    fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(equivalent(Y, Z), equivalent(W, Z)))), equivalent(X, equivalent(Y, W)))), true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W))))
% 255.32/32.78  = { by lemma 8 R->L }
% 255.32/32.78    fresh2(fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, W)), equivalent(X, equivalent(Y, W)))), true, equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(equivalent(Y, Z), equivalent(W, Z)))), equivalent(X, equivalent(Y, W)))), true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W))))
% 255.32/32.78  = { by lemma 17 }
% 255.32/32.78    fresh2(fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(equivalent(Y, Z), equivalent(W, Z)))), equivalent(X, equivalent(Y, W)))), true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W))))
% 255.32/32.78  = { by axiom 1 (condensed_detachment) }
% 255.32/32.78    fresh2(true, true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W))))
% 255.32/32.78  = { by axiom 1 (condensed_detachment) }
% 255.32/32.78    true
% 255.32/32.78  
% 255.32/32.78  Lemma 23: fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(equivalent(X, Y), W), equivalent(Z, W))) = is_a_theorem(equivalent(equivalent(equivalent(X, Y), W), equivalent(Z, W))).
% 255.32/32.78  Proof:
% 255.32/32.78    fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(equivalent(X, Y), W), equivalent(Z, W)))
% 255.32/32.78  = { by axiom 3 (condensed_detachment) R->L }
% 255.32/32.78    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, Y), W), equivalent(Z, W)))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, Y), W), equivalent(Z, W)))
% 255.32/32.78  = { by lemma 5 R->L }
% 255.32/32.78    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(X, Y), Z))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, Y), W), equivalent(Z, W)))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, Y), W), equivalent(Z, W)))
% 255.32/32.78  = { by lemma 14 }
% 255.32/32.78    fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, Y), W), equivalent(Z, W)))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, Y), W), equivalent(Z, W)))
% 255.32/32.78  = { by axiom 1 (condensed_detachment) }
% 255.32/32.78    fresh(true, true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, Y), W), equivalent(Z, W)))
% 255.32/32.78  = { by axiom 2 (condensed_detachment) }
% 255.32/32.78    is_a_theorem(equivalent(equivalent(equivalent(X, Y), W), equivalent(Z, W)))
% 255.32/32.78  
% 255.32/32.78  Lemma 24: fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z)))), true, equivalent(X, equivalent(Y, W))) = is_a_theorem(equivalent(X, equivalent(Y, W))).
% 255.32/32.78  Proof:
% 255.32/32.78    fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z)))), true, equivalent(X, equivalent(Y, W)))
% 255.32/32.78  = { by axiom 3 (condensed_detachment) R->L }
% 255.32/32.78    fresh(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W)))), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W)))
% 255.32/32.78  = { by lemma 22 }
% 255.32/32.78    fresh(true, true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W)))
% 255.32/32.78  = { by axiom 2 (condensed_detachment) }
% 255.74/32.78    is_a_theorem(equivalent(X, equivalent(Y, W)))
% 255.74/32.78  
% 255.74/32.78  Goal 1 (prove_lg_2): is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))) = true.
% 255.74/32.78  Proof:
% 255.74/32.78    is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.78  = { by axiom 2 (condensed_detachment) R->L }
% 255.74/32.78    fresh(true, true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.78  = { by axiom 1 (condensed_detachment) R->L }
% 255.74/32.79    fresh(fresh2(true, true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.79  = { by axiom 1 (condensed_detachment) R->L }
% 255.74/32.79    fresh(fresh2(fresh2(true, true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.79  = { by axiom 1 (condensed_detachment) R->L }
% 255.74/32.79    fresh(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.79  = { by axiom 1 (condensed_detachment) R->L }
% 255.74/32.79    fresh(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.79  = { by lemma 22 R->L }
% 255.74/32.79    fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(c, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e))))), true, equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.79  = { by axiom 3 (condensed_detachment) R->L }
% 255.74/32.80    fresh(fresh2(fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(c, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(c, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.80  = { by lemma 23 R->L }
% 255.74/32.80    fresh(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(c, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(c, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(c, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.81  = { by lemma 20 }
% 255.74/32.81    fresh(fresh2(fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(c, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(c, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.81  = { by axiom 1 (condensed_detachment) }
% 255.74/32.81    fresh(fresh2(fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(c, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.81  = { by axiom 2 (condensed_detachment) }
% 255.74/32.81    fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(c, e), equivalent(b, e))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.81  = { by lemma 13 }
% 255.74/32.81    fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.81  = { by lemma 24 }
% 255.74/32.81    fresh(fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.81  = { by lemma 24 }
% 255.74/32.81    fresh(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.81  = { by axiom 3 (condensed_detachment) }
% 255.74/32.81    fresh2(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.81  = { by axiom 2 (condensed_detachment) R->L }
% 255.74/32.81    fresh2(fresh(true, true, equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 255.74/32.81  = { by axiom 1 (condensed_detachment) R->L }
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% 255.74/32.81  = { by axiom 1 (condensed_detachment) R->L }
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% 255.74/32.81  = { by axiom 1 (condensed_detachment) R->L }
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% 255.74/32.82  = { by axiom 4 (s_2) R->L }
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% 255.74/32.82  = { by lemma 23 }
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% 255.74/32.82  = { by lemma 10 }
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% 255.74/32.83  = { by axiom 3 (condensed_detachment) R->L }
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% 255.74/32.83  = { by axiom 2 (condensed_detachment) R->L }
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% 255.74/32.84  = { by axiom 1 (condensed_detachment) R->L }
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% 256.26/32.86  = { by lemma 18 R->L }
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% 256.39/32.89  = { by lemma 5 R->L }
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% 256.74/32.92  = { by axiom 2 (condensed_detachment) }
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% 256.74/32.93  = { by axiom 3 (condensed_detachment) }
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% 256.74/32.93  = { by lemma 19 R->L }
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% 256.74/32.94  = { by lemma 17 }
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% 256.74/32.94  = { by axiom 1 (condensed_detachment) }
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% 256.98/32.94  = { by axiom 1 (condensed_detachment) }
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% 256.98/32.94  = { by axiom 2 (condensed_detachment) }
% 256.98/32.94    fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.94  = { by axiom 3 (condensed_detachment) }
% 256.98/32.94    fresh2(fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.95  = { by axiom 2 (condensed_detachment) R->L }
% 256.98/32.95    fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.95  = { by axiom 1 (condensed_detachment) R->L }
% 256.98/32.95    fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.95  = { by axiom 1 (condensed_detachment) R->L }
% 256.98/32.95    fresh2(fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(b, c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.95  = { by lemma 20 R->L }
% 256.98/32.95    fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(b, c)), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(b, c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.95  = { by lemma 13 }
% 256.98/32.96    fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(b, c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.96  = { by axiom 3 (condensed_detachment) R->L }
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% 256.98/32.96  = { by lemma 23 R->L }
% 256.98/32.96    fresh2(fresh2(fresh(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(b, c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(b, c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(b, c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.96  = { by lemma 16 }
% 256.98/32.96    fresh2(fresh2(fresh(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(b, c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(b, c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.96  = { by axiom 1 (condensed_detachment) }
% 256.98/32.96    fresh2(fresh2(fresh(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(b, c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.96  = { by axiom 2 (condensed_detachment) }
% 256.98/32.96    fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.96  = { by axiom 3 (condensed_detachment) }
% 256.98/32.96    fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))))), true, equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.96  = { by lemma 21 R->L }
% 256.98/32.96    fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(equivalent(c, c), equivalent(b, c)), equivalent(equivalent(c, c), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))))), true, equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.96  = { by lemma 9 }
% 256.98/32.97    fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, c), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))))), true, equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.97  = { by axiom 1 (condensed_detachment) }
% 256.98/32.97    fresh2(fresh2(fresh2(true, true, equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(b, c)))), true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.97  = { by axiom 1 (condensed_detachment) }
% 256.98/32.97    fresh2(fresh2(true, true, equivalent(a, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(c, e), equivalent(b, e))), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.97  = { by axiom 1 (condensed_detachment) }
% 256.98/32.97    fresh2(true, true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 256.98/32.97  = { by axiom 1 (condensed_detachment) }
% 256.98/32.97    true
% 256.98/32.97  % SZS output end Proof
% 256.98/32.97  
% 256.98/32.97  RESULT: Unsatisfiable (the axioms are contradictory).
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