%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL121-1 : 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 : n029.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 08:17:33 EDT 2023

% Result   : Unsatisfiable 6.64s 1.27s
% Output   : Proof 7.96s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL121-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34  % Computer : n029.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug 24 18:08:53 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 6.64/1.27  Command-line arguments: --no-flatten-goal
% 6.64/1.27  
% 6.64/1.27  % SZS status Unsatisfiable
% 6.64/1.27  
% 7.26/1.31  % SZS output start Proof
% 7.26/1.31  Take the following subset of the input axioms:
% 7.26/1.31    fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 7.26/1.31    fof(lg_2, axiom, ![Z, U, X2, Y2]: is_a_theorem(equivalent(X2, equivalent(X2, equivalent(equivalent(Y2, Z), equivalent(equivalent(Y2, U), equivalent(Z, U))))))).
% 7.26/1.31    fof(prove_lg_1, negated_conjecture, ~is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))).
% 7.26/1.31  
% 7.26/1.31  Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.26/1.31  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.26/1.31  We repeatedly replace C & s=t => u=v by the two clauses:
% 7.26/1.31    fresh(y, y, x1...xn) = u
% 7.26/1.31    C => fresh(s, t, x1...xn) = v
% 7.26/1.31  where fresh is a fresh function symbol and x1..xn are the free
% 7.26/1.31  variables of u and v.
% 7.26/1.31  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.26/1.31  input problem has no model of domain size 1).
% 7.26/1.31  
% 7.26/1.31  The encoding turns the above axioms into the following unit equations and goals:
% 7.26/1.31  
% 7.26/1.31  Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 7.26/1.31  Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 7.26/1.31  Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 7.26/1.31  Axiom 4 (lg_2): is_a_theorem(equivalent(X, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W)))))) = true.
% 7.26/1.31  
% 7.26/1.31  Lemma 5: is_a_theorem(equivalent(equivalent(X, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W))))), equivalent(equivalent(V, U), equivalent(equivalent(V, T), equivalent(U, T))))) = true.
% 7.26/1.31  Proof:
% 7.26/1.31    is_a_theorem(equivalent(equivalent(X, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W))))), equivalent(equivalent(V, U), equivalent(equivalent(V, T), equivalent(U, T)))))
% 7.26/1.31  = { by axiom 2 (condensed_detachment) R->L }
% 7.26/1.31    fresh(true, true, equivalent(X, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W))))), equivalent(equivalent(X, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W))))), equivalent(equivalent(V, U), equivalent(equivalent(V, T), equivalent(U, T)))))
% 7.26/1.31  = { by axiom 4 (lg_2) R->L }
% 7.26/1.31    fresh(is_a_theorem(equivalent(equivalent(X, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W))))), equivalent(equivalent(X, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W))))), equivalent(equivalent(V, U), equivalent(equivalent(V, T), equivalent(U, T)))))), true, equivalent(X, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W))))), equivalent(equivalent(X, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W))))), equivalent(equivalent(V, U), equivalent(equivalent(V, T), equivalent(U, T)))))
% 7.26/1.31  = { by axiom 3 (condensed_detachment) }
% 7.26/1.31    fresh2(is_a_theorem(equivalent(X, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W)))))), true, equivalent(equivalent(X, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W))))), equivalent(equivalent(V, U), equivalent(equivalent(V, T), equivalent(U, T)))))
% 7.26/1.31  = { by axiom 4 (lg_2) }
% 7.26/1.31    fresh2(true, true, equivalent(equivalent(X, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W))))), equivalent(equivalent(V, U), equivalent(equivalent(V, T), equivalent(U, T)))))
% 7.26/1.31  = { by axiom 1 (condensed_detachment) }
% 7.26/1.31    true
% 7.26/1.31  
% 7.26/1.31  Lemma 6: is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))) = true.
% 7.26/1.31  Proof:
% 7.26/1.31    is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 7.26/1.31  = { by axiom 2 (condensed_detachment) R->L }
% 7.26/1.31    fresh(true, true, equivalent(W, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(V, T), equivalent(U, T))))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 7.26/1.31  = { by lemma 5 R->L }
% 7.26/1.31    fresh(is_a_theorem(equivalent(equivalent(W, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(V, T), equivalent(U, T))))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))), true, equivalent(W, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(V, T), equivalent(U, T))))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 7.26/1.31  = { by axiom 3 (condensed_detachment) }
% 7.26/1.31    fresh2(is_a_theorem(equivalent(W, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(V, T), equivalent(U, T)))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 7.26/1.31  = { by axiom 4 (lg_2) }
% 7.26/1.32    fresh2(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 7.26/1.32  = { by axiom 1 (condensed_detachment) }
% 7.26/1.32    true
% 7.26/1.32  
% 7.26/1.32  Lemma 7: 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))).
% 7.26/1.32  Proof:
% 7.26/1.32    fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(X, Z), equivalent(Y, Z)))
% 7.26/1.32  = { by axiom 3 (condensed_detachment) R->L }
% 7.26/1.32    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)))
% 7.26/1.32  = { by lemma 6 }
% 7.26/1.32    fresh(true, true, equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))
% 7.26/1.32  = { by axiom 2 (condensed_detachment) }
% 7.26/1.32    is_a_theorem(equivalent(equivalent(X, Z), equivalent(Y, Z)))
% 7.26/1.32  
% 7.26/1.32  Lemma 8: is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))) = true.
% 7.26/1.32  Proof:
% 7.26/1.32    is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z)))
% 7.26/1.32  = { by lemma 7 R->L }
% 7.26/1.32    fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, W), equivalent(Y, W)))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z)))
% 7.26/1.32  = { by lemma 6 }
% 7.26/1.32    fresh2(true, true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z)))
% 7.26/1.32  = { by axiom 1 (condensed_detachment) }
% 7.26/1.32    true
% 7.26/1.32  
% 7.26/1.32  Lemma 9: 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)).
% 7.26/1.32  Proof:
% 7.26/1.32    fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 7.26/1.32  = { by axiom 3 (condensed_detachment) R->L }
% 7.26/1.32    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))
% 7.26/1.32  = { by lemma 8 }
% 7.26/1.32    fresh(true, true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 7.26/1.32  = { by axiom 2 (condensed_detachment) }
% 7.26/1.32    is_a_theorem(equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 7.26/1.32  
% 7.26/1.32  Lemma 10: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W)))) = true.
% 7.26/1.32  Proof:
% 7.26/1.32    is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 7.26/1.32  = { by lemma 9 R->L }
% 7.26/1.32    fresh2(is_a_theorem(equivalent(equivalent(X, Z), equivalent(equivalent(X, W), equivalent(Z, W)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 7.26/1.32  = { by lemma 6 }
% 7.26/1.32    fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 7.26/1.32  = { by axiom 1 (condensed_detachment) }
% 7.26/1.32    true
% 7.26/1.32  
% 7.26/1.32  Lemma 11: 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))).
% 7.26/1.32  Proof:
% 7.26/1.32    fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, Y))), true, equivalent(equivalent(X, W), equivalent(Z, W)))
% 7.26/1.32  = { by axiom 3 (condensed_detachment) R->L }
% 7.26/1.32    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)))
% 7.26/1.32  = { by lemma 10 }
% 7.26/1.32    fresh(true, true, equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W)))
% 7.26/1.32  = { by axiom 2 (condensed_detachment) }
% 7.26/1.32    is_a_theorem(equivalent(equivalent(X, W), equivalent(Z, W)))
% 7.26/1.32  
% 7.26/1.32  Lemma 12: fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z))), true, equivalent(equivalent(X, Y), W)) = is_a_theorem(equivalent(equivalent(X, Y), W)).
% 7.26/1.32  Proof:
% 7.26/1.32    fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z))), true, equivalent(equivalent(X, Y), W))
% 7.26/1.32  = { by axiom 3 (condensed_detachment) R->L }
% 7.26/1.32    fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z)), equivalent(equivalent(X, Y), W))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z)), equivalent(equivalent(X, Y), W))
% 7.26/1.32  = { by lemma 9 R->L }
% 7.26/1.32    fresh(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))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z)), equivalent(equivalent(X, Y), W))
% 7.26/1.32  = { by lemma 11 R->L }
% 7.26/1.32    fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(V, Y)), equivalent(equivalent(X, Y), equivalent(V, Y)))), true, 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))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z)), equivalent(equivalent(X, Y), W))
% 7.26/1.32  = { by lemma 10 }
% 7.26/1.32    fresh(fresh2(fresh2(true, true, 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))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z)), equivalent(equivalent(X, Y), W))
% 7.26/1.32  = { by axiom 1 (condensed_detachment) }
% 7.26/1.32    fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z)), equivalent(equivalent(X, Y), W))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z)), equivalent(equivalent(X, Y), W))
% 7.26/1.32  = { by axiom 1 (condensed_detachment) }
% 7.26/1.32    fresh(true, true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(W, Z)), equivalent(equivalent(X, Y), W))
% 7.26/1.32  = { by axiom 2 (condensed_detachment) }
% 7.26/1.32    is_a_theorem(equivalent(equivalent(X, Y), W))
% 7.26/1.32  
% 7.26/1.32  Lemma 13: is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Y))) = true.
% 7.26/1.32  Proof:
% 7.26/1.32    is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Y)))
% 7.26/1.32  = { by lemma 12 R->L }
% 7.26/1.32    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)))
% 7.26/1.32  = { by lemma 10 }
% 7.26/1.32    fresh2(true, true, equivalent(equivalent(X, Y), equivalent(X, Y)))
% 7.26/1.32  = { by axiom 1 (condensed_detachment) }
% 7.26/1.32    true
% 7.26/1.32  
% 7.26/1.32  Lemma 14: is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W)))) = true.
% 7.26/1.32  Proof:
% 7.26/1.32    is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W))))
% 7.26/1.32  = { by lemma 12 R->L }
% 7.26/1.32    fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(equivalent(Y, W), equivalent(equivalent(Y, Z), equivalent(W, Z))))), equivalent(equivalent(X, equivalent(Y, W)), equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(equivalent(Y, W), equivalent(equivalent(Y, Z), equivalent(W, Z))))))), true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W))))
% 7.26/1.32  = { by lemma 5 }
% 7.26/1.32    fresh2(true, true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W))))
% 7.26/1.32  = { by axiom 1 (condensed_detachment) }
% 7.26/1.32    true
% 7.26/1.32  
% 7.26/1.32  Lemma 15: 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))).
% 7.26/1.32  Proof:
% 7.26/1.32    fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z)))), true, equivalent(X, equivalent(Y, W)))
% 7.26/1.32  = { by axiom 3 (condensed_detachment) R->L }
% 7.26/1.32    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)))
% 7.26/1.32  = { by lemma 14 }
% 7.26/1.32    fresh(true, true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(X, equivalent(Y, W)))
% 7.26/1.32  = { by axiom 2 (condensed_detachment) }
% 7.26/1.32    is_a_theorem(equivalent(X, equivalent(Y, W)))
% 7.26/1.32  
% 7.26/1.32  Lemma 16: 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)).
% 7.26/1.32  Proof:
% 7.26/1.32    fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W)), true, equivalent(equivalent(X, Z), W))
% 7.26/1.32  = { by axiom 3 (condensed_detachment) R->L }
% 7.26/1.32    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))
% 7.26/1.32  = { by lemma 7 R->L }
% 7.26/1.32    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))
% 7.26/1.32  = { by lemma 9 R->L }
% 7.26/1.32    fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(X, Z), equivalent(X, Z))), true, 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))
% 7.26/1.32  = { by lemma 13 }
% 7.26/1.32    fresh(fresh2(fresh2(true, true, 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))
% 7.26/1.32  = { by axiom 1 (condensed_detachment) }
% 7.26/1.32    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))
% 7.26/1.32  = { by axiom 1 (condensed_detachment) }
% 7.26/1.32    fresh(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))
% 7.26/1.32  = { by axiom 2 (condensed_detachment) }
% 7.26/1.32    is_a_theorem(equivalent(equivalent(X, Z), W))
% 7.26/1.32  
% 7.26/1.32  Lemma 17: is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(X, Y))) = true.
% 7.26/1.32  Proof:
% 7.26/1.32    is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(X, Y)))
% 7.26/1.32  = { by lemma 15 R->L }
% 7.26/1.32    fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(equivalent(X, equivalent(Z, Z)), equivalent(Y, equivalent(Z, Z))))), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(X, Y)))
% 7.26/1.32  = { by lemma 11 R->L }
% 7.26/1.32    fresh2(fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(W, Z)), equivalent(equivalent(X, equivalent(Z, Z)), equivalent(W, Z)))), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(equivalent(X, equivalent(Z, Z)), equivalent(Y, equivalent(Z, Z))))), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(X, Y)))
% 7.26/1.32  = { by lemma 16 R->L }
% 7.26/1.32    fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Z, Z)), equivalent(equivalent(W, Z), equivalent(Z, Z))), equivalent(equivalent(X, equivalent(Z, Z)), equivalent(W, Z)))), true, equivalent(equivalent(X, equivalent(W, Z)), equivalent(equivalent(X, equivalent(Z, Z)), equivalent(W, Z)))), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(equivalent(X, equivalent(Z, Z)), equivalent(Y, equivalent(Z, Z))))), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(X, Y)))
% 7.26/1.32  = { by lemma 14 }
% 7.26/1.32    fresh2(fresh2(fresh2(true, true, equivalent(equivalent(X, equivalent(W, Z)), equivalent(equivalent(X, equivalent(Z, Z)), equivalent(W, Z)))), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(equivalent(X, equivalent(Z, Z)), equivalent(Y, equivalent(Z, Z))))), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(X, Y)))
% 7.26/1.32  = { by axiom 1 (condensed_detachment) }
% 7.26/1.32    fresh2(fresh2(true, true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(equivalent(X, equivalent(Z, Z)), equivalent(Y, equivalent(Z, Z))))), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(X, Y)))
% 7.26/1.32  = { by axiom 1 (condensed_detachment) }
% 7.26/1.32    fresh2(true, true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(X, Y)))
% 7.26/1.32  = { by axiom 1 (condensed_detachment) }
% 7.26/1.33    true
% 7.26/1.33  
% 7.26/1.33  Goal 1 (prove_lg_1): is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))) = true.
% 7.26/1.33  Proof:
% 7.26/1.33    is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by axiom 2 (condensed_detachment) R->L }
% 7.26/1.33    fresh(true, true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by axiom 1 (condensed_detachment) R->L }
% 7.26/1.33    fresh(fresh2(true, true, equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by axiom 1 (condensed_detachment) R->L }
% 7.26/1.33    fresh(fresh2(fresh2(true, true, equivalent(equivalent(a, equivalent(b, b)), a)), true, equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by lemma 13 R->L }
% 7.26/1.33    fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(b, b)))), true, equivalent(equivalent(a, equivalent(b, b)), a)), true, equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by axiom 3 (condensed_detachment) R->L }
% 7.26/1.33    fresh(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(b, b)), a))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(b, b)), a)), true, equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by lemma 17 }
% 7.26/1.33    fresh(fresh2(fresh(true, true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(b, b)), a)), true, equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by axiom 2 (condensed_detachment) }
% 7.26/1.33    fresh(fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(b, b)), a)), true, equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by lemma 7 }
% 7.26/1.33    fresh(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by axiom 3 (condensed_detachment) }
% 7.26/1.33    fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by lemma 16 R->L }
% 7.26/1.33    fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by axiom 2 (condensed_detachment) R->L }
% 7.26/1.33    fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by axiom 1 (condensed_detachment) R->L }
% 7.26/1.33    fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by axiom 1 (condensed_detachment) R->L }
% 7.26/1.33    fresh2(fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.33  = { by lemma 6 R->L }
% 7.26/1.33    fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.34  = { by axiom 3 (condensed_detachment) R->L }
% 7.26/1.34    fresh2(fresh2(fresh(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.34  = { by lemma 7 R->L }
% 7.26/1.34    fresh2(fresh2(fresh(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.34  = { by axiom 4 (lg_2) }
% 7.26/1.34    fresh2(fresh2(fresh(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.34  = { by axiom 1 (condensed_detachment) }
% 7.26/1.34    fresh2(fresh2(fresh(fresh2(fresh(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.34  = { by axiom 2 (condensed_detachment) }
% 7.26/1.34    fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.35  = { by lemma 11 }
% 7.26/1.35    fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.35  = { by axiom 3 (condensed_detachment) }
% 7.26/1.35    fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.35  = { by axiom 2 (condensed_detachment) R->L }
% 7.26/1.35    fresh2(fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.35  = { by axiom 1 (condensed_detachment) R->L }
% 7.26/1.35    fresh2(fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.35  = { by lemma 17 R->L }
% 7.26/1.35    fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.35  = { by lemma 15 }
% 7.26/1.35    fresh2(fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.35  = { by axiom 3 (condensed_detachment) }
% 7.26/1.35    fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.35  = { by lemma 15 R->L }
% 7.26/1.35    fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.36  = { by axiom 2 (condensed_detachment) R->L }
% 7.26/1.36    fresh2(fresh2(fresh2(fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.36  = { by axiom 1 (condensed_detachment) R->L }
% 7.26/1.36    fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.36  = { by lemma 6 R->L }
% 7.26/1.36    fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.26/1.37  = { by axiom 3 (condensed_detachment) R->L }
% 7.26/1.37    fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), 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% 7.26/1.37  = { by lemma 7 R->L }
% 7.96/1.37    fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, 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equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.96/1.38  = { by lemma 8 }
% 7.96/1.38    fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.96/1.38  = { by axiom 1 (condensed_detachment) }
% 7.96/1.38    fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.96/1.38  = { by axiom 2 (condensed_detachment) }
% 7.96/1.38    fresh2(fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.96/1.39  = { by axiom 3 (condensed_detachment) }
% 7.96/1.39    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(b, equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.96/1.39  = { by lemma 14 }
% 7.96/1.39    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(b, equivalent(c, c))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.96/1.39  = { by axiom 1 (condensed_detachment) }
% 7.96/1.39    fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(c, c), equivalent(b, equivalent(c, c)))), equivalent(c, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.96/1.39  = { by axiom 1 (condensed_detachment) }
% 7.96/1.39    fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(b, equivalent(b, equivalent(c, c)))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.96/1.39  = { by axiom 1 (condensed_detachment) }
% 7.96/1.39    fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)), equivalent(equivalent(b, b), equivalent(equivalent(b, equivalent(c, c)), b))), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.96/1.39  = { by axiom 1 (condensed_detachment) }
% 7.96/1.39    fresh2(fresh2(true, true, equivalent(equivalent(a, equivalent(b, b)), equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b)))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.96/1.39  = { by axiom 1 (condensed_detachment) }
% 7.96/1.39    fresh2(true, true, equivalent(a, equivalent(a, equivalent(equivalent(b, equivalent(c, c)), b))))
% 7.96/1.39  = { by axiom 1 (condensed_detachment) }
% 7.96/1.39    true
% 7.96/1.39  % SZS output end Proof
% 7.96/1.39  
% 7.96/1.39  RESULT: Unsatisfiable (the axioms are contradictory).
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