%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL128-1 : 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 : n005.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 15.74s 2.31s
% Output   : Proof 18.11s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : LCL128-1 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.11  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.30  % Computer : n005.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Fri Aug 25 04:43:08 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 15.74/2.31  Command-line arguments: --no-flatten-goal
% 15.74/2.31  
% 15.74/2.31  % SZS status Unsatisfiable
% 15.74/2.31  
% 16.41/2.42  % SZS output start Proof
% 16.41/2.42  Take the following subset of the input axioms:
% 16.41/2.42    fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 16.41/2.42    fof(prove_lg_2, negated_conjecture, ~is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))).
% 16.41/2.42    fof(s_3, axiom, ![Z, U, X2, Y2]: is_a_theorem(equivalent(X2, equivalent(X2, equivalent(equivalent(equivalent(Y2, Z), equivalent(U, Z)), equivalent(Y2, U)))))).
% 16.41/2.42  
% 16.41/2.42  Now clausify the problem and encode Horn clauses using encoding 3 of
% 16.41/2.42  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 16.41/2.42  We repeatedly replace C & s=t => u=v by the two clauses:
% 16.41/2.42    fresh(y, y, x1...xn) = u
% 16.41/2.42    C => fresh(s, t, x1...xn) = v
% 16.41/2.42  where fresh is a fresh function symbol and x1..xn are the free
% 16.41/2.42  variables of u and v.
% 16.41/2.42  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 16.41/2.42  input problem has no model of domain size 1).
% 16.41/2.42  
% 16.41/2.42  The encoding turns the above axioms into the following unit equations and goals:
% 16.41/2.42  
% 16.41/2.42  Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 16.41/2.42  Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 16.41/2.42  Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 16.41/2.42  Axiom 4 (s_3): is_a_theorem(equivalent(X, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))))) = true.
% 16.41/2.42  
% 16.41/2.42  Lemma 5: fresh2(is_a_theorem(X), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)))) = is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)))).
% 16.41/2.42  Proof:
% 16.41/2.42    fresh2(is_a_theorem(X), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))))
% 16.41/2.42  = { by axiom 3 (condensed_detachment) R->L }
% 16.41/2.42    fresh(is_a_theorem(equivalent(X, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))))), true, X, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))))
% 16.41/2.42  = { by axiom 4 (s_3) }
% 16.41/2.42    fresh(true, true, X, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))))
% 16.41/2.42  = { by axiom 2 (condensed_detachment) }
% 16.41/2.42    is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))))
% 16.41/2.42  
% 16.41/2.42  Lemma 6: is_a_theorem(equivalent(equivalent(X, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)))), equivalent(equivalent(equivalent(V, U), equivalent(T, U)), equivalent(V, T)))) = true.
% 16.41/2.42  Proof:
% 16.41/2.42    is_a_theorem(equivalent(equivalent(X, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)))), equivalent(equivalent(equivalent(V, U), equivalent(T, U)), equivalent(V, T))))
% 16.41/2.42  = { by lemma 5 R->L }
% 16.41/2.42    fresh2(is_a_theorem(equivalent(X, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))))), true, equivalent(equivalent(X, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)))), equivalent(equivalent(equivalent(V, U), equivalent(T, U)), equivalent(V, T))))
% 16.41/2.42  = { by axiom 4 (s_3) }
% 16.41/2.42    fresh2(true, true, equivalent(equivalent(X, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)))), equivalent(equivalent(equivalent(V, U), equivalent(T, U)), equivalent(V, T))))
% 16.41/2.42  = { by axiom 1 (condensed_detachment) }
% 16.41/2.42    true
% 16.41/2.42  
% 16.41/2.42  Lemma 7: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z))) = true.
% 16.41/2.42  Proof:
% 16.41/2.42    is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)))
% 16.41/2.42  = { by axiom 2 (condensed_detachment) R->L }
% 16.41/2.42    fresh(true, true, equivalent(W, equivalent(W, equivalent(equivalent(equivalent(V, U), equivalent(T, U)), equivalent(V, T)))), equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)))
% 16.41/2.42  = { by lemma 6 R->L }
% 16.41/2.42    fresh(is_a_theorem(equivalent(equivalent(W, equivalent(W, equivalent(equivalent(equivalent(V, U), equivalent(T, U)), equivalent(V, T)))), equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)))), true, equivalent(W, equivalent(W, equivalent(equivalent(equivalent(V, U), equivalent(T, U)), equivalent(V, T)))), equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)))
% 16.41/2.42  = { by axiom 3 (condensed_detachment) }
% 16.41/2.42    fresh2(is_a_theorem(equivalent(W, equivalent(W, equivalent(equivalent(equivalent(V, U), equivalent(T, U)), equivalent(V, T))))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)))
% 16.41/2.42  = { by axiom 4 (s_3) }
% 16.41/2.42    fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)))
% 16.41/2.42  = { by axiom 1 (condensed_detachment) }
% 16.41/2.42    true
% 16.41/2.42  
% 16.41/2.42  Lemma 8: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, Y))), true, equivalent(X, Z)) = is_a_theorem(equivalent(X, Z)).
% 16.41/2.42  Proof:
% 16.41/2.43    fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, Y))), true, equivalent(X, Z))
% 16.41/2.43  = { by axiom 3 (condensed_detachment) R->L }
% 16.41/2.43    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z))), true, equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z))
% 16.41/2.43  = { by lemma 7 }
% 16.41/2.43    fresh(true, true, equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z))
% 16.41/2.43  = { by axiom 2 (condensed_detachment) }
% 16.41/2.43    is_a_theorem(equivalent(X, Z))
% 16.41/2.43  
% 16.41/2.43  Lemma 9: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W)))) = true.
% 16.41/2.43  Proof:
% 16.41/2.43    is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 16.41/2.43  = { by lemma 8 R->L }
% 16.41/2.43    fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)), equivalent(equivalent(equivalent(X, W), equivalent(Z, W)), equivalent(X, Z)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 16.41/2.43  = { by lemma 5 R->L }
% 16.41/2.43    fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)), equivalent(equivalent(equivalent(X, W), equivalent(Z, W)), equivalent(X, Z)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 16.41/2.43  = { by lemma 7 }
% 16.41/2.43    fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)), equivalent(equivalent(equivalent(X, W), equivalent(Z, W)), equivalent(X, Z)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 16.41/2.43  = { by axiom 1 (condensed_detachment) }
% 16.41/2.43    fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 16.41/2.43  = { by axiom 1 (condensed_detachment) }
% 16.41/2.43    true
% 16.41/2.43  
% 16.41/2.43  Lemma 10: is_a_theorem(equivalent(X, X)) = true.
% 16.41/2.43  Proof:
% 16.41/2.43    is_a_theorem(equivalent(X, X))
% 16.41/2.43  = { by lemma 8 R->L }
% 16.41/2.43    fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Y))), true, equivalent(X, X))
% 16.41/2.43  = { by lemma 8 R->L }
% 16.41/2.43    fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, Y), equivalent(Z, Y)))), true, equivalent(equivalent(X, Y), equivalent(X, Y))), true, equivalent(X, X))
% 16.41/2.43  = { by lemma 9 }
% 16.41/2.43    fresh2(fresh2(true, true, equivalent(equivalent(X, Y), equivalent(X, Y))), true, equivalent(X, X))
% 16.41/2.43  = { by axiom 1 (condensed_detachment) }
% 16.41/2.43    fresh2(true, true, equivalent(X, X))
% 16.41/2.43  = { by axiom 1 (condensed_detachment) }
% 16.41/2.43    true
% 16.41/2.43  
% 16.41/2.43  Lemma 11: is_a_theorem(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)))) = true.
% 16.41/2.43  Proof:
% 16.41/2.43    is_a_theorem(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))))
% 16.41/2.43  = { by lemma 5 R->L }
% 16.41/2.43    fresh2(is_a_theorem(equivalent(X, X)), true, equivalent(equivalent(X, X), equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))))
% 16.41/2.43  = { by lemma 10 }
% 16.41/2.43    fresh2(true, true, equivalent(equivalent(X, X), equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))))
% 16.41/2.43  = { by axiom 1 (condensed_detachment) }
% 16.41/2.43    true
% 16.41/2.43  
% 16.41/2.43  Lemma 12: is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))) = true.
% 16.41/2.43  Proof:
% 16.41/2.43    is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 16.41/2.43  = { by lemma 8 R->L }
% 16.41/2.43    fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Y)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 16.41/2.43  = { by lemma 11 }
% 16.41/2.43    fresh2(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 16.41/2.43  = { by axiom 1 (condensed_detachment) }
% 16.41/2.43    true
% 16.41/2.43  
% 16.41/2.43  Lemma 13: fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(X, Z), equivalent(Y, Z))) = is_a_theorem(equivalent(equivalent(X, Z), equivalent(Y, Z))).
% 16.41/2.43  Proof:
% 16.41/2.43    fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(X, Z), equivalent(Y, Z)))
% 16.41/2.43  = { by axiom 3 (condensed_detachment) R->L }
% 16.41/2.43    fresh(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))), true, equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))
% 16.41/2.43  = { by lemma 12 }
% 16.41/2.43    fresh(true, true, equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))
% 16.41/2.43  = { by axiom 2 (condensed_detachment) }
% 16.41/2.43    is_a_theorem(equivalent(equivalent(X, Z), equivalent(Y, Z)))
% 16.41/2.43  
% 16.41/2.43  Lemma 14: fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W)), true, equivalent(equivalent(X, Z), W)) = is_a_theorem(equivalent(equivalent(X, Z), W)).
% 16.41/2.43  Proof:
% 16.41/2.43    fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W)), true, equivalent(equivalent(X, Z), W))
% 16.41/2.43  = { by axiom 3 (condensed_detachment) R->L }
% 16.41/2.43    fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))
% 16.41/2.43  = { by lemma 13 R->L }
% 16.41/2.43    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))
% 16.41/2.43  = { by lemma 7 }
% 16.41/2.43    fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))
% 16.41/2.43  = { by axiom 1 (condensed_detachment) }
% 16.41/2.43    fresh(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))
% 16.41/2.43  = { by axiom 2 (condensed_detachment) }
% 16.41/2.43    is_a_theorem(equivalent(equivalent(X, Z), W))
% 16.41/2.43  
% 16.41/2.43  Lemma 15: is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X)) = true.
% 16.41/2.43  Proof:
% 16.41/2.43    is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X))
% 16.41/2.43  = { by lemma 14 R->L }
% 16.41/2.43    fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X)), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X))
% 16.41/2.43  = { by axiom 2 (condensed_detachment) R->L }
% 16.41/2.43    fresh2(fresh(true, true, equivalent(X, X), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X)), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X))
% 16.41/2.43  = { by axiom 1 (condensed_detachment) R->L }
% 16.41/2.43    fresh2(fresh(fresh2(true, true, equivalent(equivalent(X, X), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X))), true, equivalent(X, X), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X)), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X))
% 16.41/2.43  = { by axiom 1 (condensed_detachment) R->L }
% 16.41/2.43    fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)))), true, equivalent(equivalent(X, X), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X))), true, equivalent(X, X), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X)), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X))
% 16.41/2.43  = { by lemma 6 R->L }
% 16.41/2.43    fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)))), equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)))))), true, equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)))), true, equivalent(equivalent(X, X), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X))), true, equivalent(X, X), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X)), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X))
% 16.41/2.43  = { by lemma 8 }
% 16.41/2.44    fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)))), true, equivalent(equivalent(X, X), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X))), true, equivalent(X, X), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X)), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X))
% 16.41/2.44  = { by lemma 8 }
% 16.41/2.44    fresh2(fresh(is_a_theorem(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X))), true, equivalent(X, X), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X)), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X))
% 16.41/2.44  = { by axiom 3 (condensed_detachment) }
% 16.41/2.44    fresh2(fresh2(is_a_theorem(equivalent(X, X)), true, equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X)), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X))
% 16.41/2.44  = { by lemma 10 }
% 16.41/2.44    fresh2(fresh2(true, true, equivalent(equivalent(equivalent(X, X), equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)), X)), X)), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X))
% 16.41/2.44  = { by axiom 1 (condensed_detachment) }
% 16.41/2.44    fresh2(true, true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X))
% 16.41/2.44  = { by axiom 1 (condensed_detachment) }
% 16.41/2.44    true
% 16.41/2.44  
% 16.41/2.44  Lemma 16: is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W)))) = true.
% 16.41/2.44  Proof:
% 16.41/2.44    is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W))))
% 16.41/2.44  = { by lemma 14 R->L }
% 16.41/2.44    fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, W)), equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), equivalent(X, equivalent(Y, W)))), true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W))))
% 16.41/2.44  = { by lemma 15 }
% 16.41/2.44    fresh2(true, true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W))))
% 16.41/2.44  = { by axiom 1 (condensed_detachment) }
% 16.41/2.44    true
% 16.41/2.44  
% 16.41/2.44  Lemma 17: 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))).
% 16.41/2.44  Proof:
% 16.41/2.44    fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, Y))), true, equivalent(equivalent(X, W), equivalent(Z, W)))
% 16.41/2.44  = { by axiom 3 (condensed_detachment) R->L }
% 16.41/2.44    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)))
% 16.41/2.44  = { by lemma 9 }
% 16.41/2.44    fresh(true, true, equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W)))
% 16.41/2.44  = { by axiom 2 (condensed_detachment) }
% 16.41/2.44    is_a_theorem(equivalent(equivalent(X, W), equivalent(Z, W)))
% 16.41/2.44  
% 16.41/2.44  Lemma 18: fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)))), true, X) = is_a_theorem(X).
% 16.41/2.44  Proof:
% 16.41/2.44    fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)))), true, X)
% 16.41/2.44  = { by axiom 3 (condensed_detachment) R->L }
% 16.41/2.44    fresh(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X)
% 16.41/2.44  = { by lemma 15 }
% 16.41/2.44    fresh(true, true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X)
% 16.41/2.44  = { by axiom 2 (condensed_detachment) }
% 16.41/2.44    is_a_theorem(X)
% 16.41/2.44  
% 16.41/2.44  Lemma 19: is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), equivalent(Z, V))), Y))) = true.
% 16.41/2.44  Proof:
% 16.41/2.44    is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), equivalent(Z, V))), Y)))
% 16.41/2.44  = { by lemma 17 R->L }
% 16.41/2.44    fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), equivalent(Z, V))), equivalent(equivalent(X, equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), equivalent(Z, V))), equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), equivalent(Z, V))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(X, equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), equivalent(Z, V))), Y)))
% 16.41/2.44  = { by axiom 4 (s_3) }
% 16.41/2.44    fresh2(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(X, equivalent(equivalent(equivalent(Z, W), equivalent(V, W)), equivalent(Z, V))), Y)))
% 16.41/2.44  = { by axiom 1 (condensed_detachment) }
% 16.41/2.44    true
% 16.41/2.44  
% 16.41/2.44  Goal 1 (prove_lg_2): is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))) = true.
% 16.41/2.44  Proof:
% 16.41/2.44    is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 16.41/2.44  = { by axiom 2 (condensed_detachment) R->L }
% 16.41/2.44    fresh(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 16.41/2.45  = { by axiom 1 (condensed_detachment) R->L }
% 16.41/2.45    fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 16.41/2.45  = { by axiom 1 (condensed_detachment) R->L }
% 16.41/2.45    fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 16.41/2.46  = { by axiom 1 (condensed_detachment) R->L }
% 16.41/2.46    fresh(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(b, c), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 16.41/2.46  = { by axiom 1 (condensed_detachment) R->L }
% 16.41/2.46    fresh(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, c), equivalent(b, c)), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(b, c), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 16.41/2.47  = { by lemma 19 R->L }
% 16.41/2.47    fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, c), equivalent(b, c)), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, c), equivalent(b, c)), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, c), equivalent(b, c)), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, c), equivalent(b, c)), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(b, c), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 16.41/2.48  = { by lemma 18 }
% 16.41/2.48    fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, c), equivalent(b, c)), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(b, c), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 17.17/2.48  = { by axiom 3 (condensed_detachment) R->L }
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% 17.17/2.49  = { by lemma 16 }
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% 17.29/2.50  = { by axiom 2 (condensed_detachment) }
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% 17.29/2.50  = { by axiom 3 (condensed_detachment) R->L }
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% 17.43/2.52  = { by lemma 18 R->L }
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% 17.43/2.54  = { by axiom 2 (condensed_detachment) R->L }
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% 17.43/2.56  = { by axiom 1 (condensed_detachment) R->L }
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% 18.11/2.71  = { by axiom 1 (condensed_detachment) }
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% 18.11/2.71  = { by axiom 1 (condensed_detachment) }
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% 18.11/2.72  = { by axiom 2 (condensed_detachment) }
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% 18.11/2.73  = { by axiom 3 (condensed_detachment) R->L }
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% 18.11/2.74  = { by lemma 18 R->L }
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% 18.11/2.75  = { by lemma 13 R->L }
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% 18.11/2.75  = { by lemma 17 R->L }
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% 18.11/2.77  = { by axiom 1 (condensed_detachment) }
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e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 18.11/2.78  = { by axiom 1 (condensed_detachment) }
% 18.11/2.78    fresh(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 18.11/2.78  = { by axiom 1 (condensed_detachment) }
% 18.11/2.78    fresh(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 18.11/2.78  = { by axiom 2 (condensed_detachment) }
% 18.11/2.78    fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 18.11/2.78  = { by axiom 3 (condensed_detachment) }
% 18.11/2.78    fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 18.11/2.78  = { by axiom 2 (condensed_detachment) R->L }
% 18.11/2.78    fresh2(fresh(true, true, equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 18.11/2.78  = { by lemma 19 R->L }
% 18.11/2.79    fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 18.11/2.79  = { by axiom 3 (condensed_detachment) }
% 18.11/2.79    fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 18.11/2.79  = { by lemma 7 }
% 18.11/2.79    fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 18.11/2.79  = { by axiom 1 (condensed_detachment) }
% 18.11/2.79    fresh2(true, true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 18.11/2.79  = { by axiom 1 (condensed_detachment) }
% 18.11/2.79    true
% 18.11/2.79  % SZS output end Proof
% 18.11/2.79  
% 18.11/2.79  RESULT: Unsatisfiable (the axioms are contradictory).
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