%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL096-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 08:17:24 EDT 2023

% Result   : Unsatisfiable 7.65s 1.34s
% Output   : Proof 9.48s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL096-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35  % Computer : n007.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug 24 19:29:55 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 7.65/1.34  Command-line arguments: --no-flatten-goal
% 7.65/1.34  
% 7.65/1.34  % SZS status Unsatisfiable
% 7.65/1.34  
% 8.06/1.42  % SZS output start Proof
% 8.06/1.42  Take the following subset of the input axioms:
% 8.06/1.42    fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 8.06/1.42    fof(lg_2, axiom, ![Z, U, X2, Y2]: is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z)), equivalent(Y2, Z)), U), U))).
% 8.06/1.42    fof(lg_3, axiom, ![V, X2, Y2, Z2, U2]: is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), U2), equivalent(equivalent(Y2, Z2), U2)), V), V))).
% 8.06/1.42    fof(lg_4, axiom, ![X2, Y2, Z2, U2, V2]: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2, Y2), Z2), U2), equivalent(equivalent(equivalent(X2, V2), Z2), equivalent(equivalent(Y2, V2), U2))))).
% 8.06/1.42    fof(prove_lg_1, negated_conjecture, ~is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))).
% 8.06/1.42  
% 8.06/1.42  Now clausify the problem and encode Horn clauses using encoding 3 of
% 8.06/1.42  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 8.06/1.42  We repeatedly replace C & s=t => u=v by the two clauses:
% 8.06/1.42    fresh(y, y, x1...xn) = u
% 8.06/1.42    C => fresh(s, t, x1...xn) = v
% 8.06/1.42  where fresh is a fresh function symbol and x1..xn are the free
% 8.06/1.42  variables of u and v.
% 8.06/1.42  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 8.06/1.42  input problem has no model of domain size 1).
% 8.06/1.42  
% 8.06/1.42  The encoding turns the above axioms into the following unit equations and goals:
% 8.06/1.42  
% 8.06/1.42  Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 8.06/1.42  Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 8.06/1.42  Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 8.06/1.42  Axiom 4 (lg_2): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)) = true.
% 8.06/1.42  Axiom 5 (lg_4): is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), W), equivalent(equivalent(equivalent(X, V), Z), equivalent(equivalent(Y, V), W)))) = true.
% 8.06/1.42  Axiom 6 (lg_3): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V), V)) = true.
% 8.06/1.42  
% 8.06/1.42  Lemma 7: fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W)), true, W) = is_a_theorem(W).
% 8.06/1.42  Proof:
% 8.06/1.42    fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W)), true, W)
% 8.06/1.42  = { by axiom 3 (condensed_detachment) R->L }
% 8.06/1.42    fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)
% 8.06/1.42  = { by axiom 4 (lg_2) }
% 8.06/1.42    fresh(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)
% 8.06/1.42  = { by axiom 2 (condensed_detachment) }
% 8.06/1.42    is_a_theorem(W)
% 8.06/1.42  
% 8.06/1.42  Lemma 8: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z)))) = true.
% 8.06/1.42  Proof:
% 8.06/1.42    is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z))))
% 8.06/1.42  = { by lemma 7 R->L }
% 8.06/1.42    fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, W), equivalent(X, Z)), equivalent(W, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z))))), true, equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z))))
% 8.06/1.42  = { by axiom 5 (lg_4) }
% 8.06/1.42    fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z))))
% 8.06/1.42  = { by axiom 1 (condensed_detachment) }
% 8.06/1.42    true
% 8.06/1.42  
% 8.06/1.42  Lemma 9: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, equivalent(equivalent(W, Y), equivalent(W, Z))) = is_a_theorem(equivalent(equivalent(W, Y), equivalent(W, Z))).
% 8.06/1.42  Proof:
% 8.06/1.42    fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, equivalent(equivalent(W, Y), equivalent(W, Z)))
% 8.06/1.42  = { by axiom 3 (condensed_detachment) R->L }
% 8.06/1.42    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z)))), true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z)))
% 8.06/1.42  = { by lemma 8 }
% 8.06/1.42    fresh(true, true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z)))
% 8.06/1.42  = { by axiom 2 (condensed_detachment) }
% 8.06/1.42    is_a_theorem(equivalent(equivalent(W, Y), equivalent(W, Z)))
% 8.06/1.42  
% 8.06/1.42  Lemma 10: is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(Y, Z)))) = true.
% 8.06/1.42  Proof:
% 8.06/1.42    is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(Y, Z))))
% 8.06/1.42  = { by lemma 9 R->L }
% 8.06/1.42    fresh2(is_a_theorem(equivalent(equivalent(equivalent(Y, W), equivalent(Y, Z)), equivalent(equivalent(Y, W), equivalent(Y, Z)))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(Y, Z))))
% 8.06/1.42  = { by lemma 8 }
% 8.06/1.42    fresh2(true, true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(Y, Z))))
% 8.06/1.42  = { by axiom 1 (condensed_detachment) }
% 8.06/1.42    true
% 8.06/1.42  
% 8.06/1.42  Lemma 11: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, equivalent(Y, Z)) = is_a_theorem(equivalent(Y, Z)).
% 8.06/1.42  Proof:
% 8.06/1.42    fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, equivalent(Y, Z))
% 8.06/1.42  = { by axiom 3 (condensed_detachment) R->L }
% 8.06/1.42    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))), true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))
% 8.06/1.42  = { by lemma 7 R->L }
% 8.06/1.42    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))), true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))
% 8.06/1.42  = { by lemma 10 }
% 8.06/1.42    fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))), true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))
% 8.06/1.42  = { by axiom 1 (condensed_detachment) }
% 8.06/1.42    fresh(true, true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))
% 8.06/1.42  = { by axiom 2 (condensed_detachment) }
% 8.06/1.42    is_a_theorem(equivalent(Y, Z))
% 8.06/1.42  
% 8.06/1.42  Lemma 12: fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V)), true, V) = is_a_theorem(V).
% 8.06/1.42  Proof:
% 8.06/1.42    fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V)), true, V)
% 8.06/1.42  = { by axiom 3 (condensed_detachment) R->L }
% 8.06/1.42    fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V), V)), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V), V)
% 8.06/1.42  = { by axiom 6 (lg_3) }
% 8.06/1.43    fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V), V)
% 8.06/1.43  = { by axiom 2 (condensed_detachment) }
% 8.06/1.43    is_a_theorem(V)
% 8.06/1.43  
% 8.06/1.43  Lemma 13: is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z)))) = true.
% 8.06/1.43  Proof:
% 8.06/1.43    is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z))))
% 8.06/1.43  = { by lemma 12 R->L }
% 8.06/1.43    fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, W), equivalent(X, Y)), equivalent(equivalent(X, W), Z)), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z))), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z)))), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z))))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z))))
% 8.06/1.43  = { by axiom 6 (lg_3) }
% 8.06/1.43    fresh2(true, true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z))))
% 8.06/1.43  = { by axiom 1 (condensed_detachment) }
% 8.06/1.43    true
% 8.06/1.43  
% 8.06/1.43  Lemma 14: is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, W), X), equivalent(W, Z)))) = true.
% 8.06/1.43  Proof:
% 8.06/1.43    is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, W), X), equivalent(W, Z))))
% 8.06/1.43  = { by lemma 7 R->L }
% 8.06/1.43    fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, W), equivalent(Y, Z)), equivalent(W, Z)), equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, W), X), equivalent(W, Z))))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, W), X), equivalent(W, Z))))
% 8.06/1.43  = { by lemma 13 }
% 8.06/1.43    fresh2(true, true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, W), X), equivalent(W, Z))))
% 8.06/1.43  = { by axiom 1 (condensed_detachment) }
% 8.06/1.43    true
% 8.06/1.43  
% 8.06/1.43  Lemma 15: is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z))) = true.
% 8.06/1.43  Proof:
% 8.06/1.43    is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)))
% 8.06/1.43  = { by axiom 2 (condensed_detachment) R->L }
% 8.06/1.43    fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)))
% 8.06/1.43  = { by axiom 1 (condensed_detachment) R->L }
% 8.06/1.43    fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)))
% 8.06/1.43  = { by lemma 10 R->L }
% 8.06/1.43    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)))
% 8.06/1.43  = { by lemma 12 }
% 8.06/1.43    fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)))
% 8.06/1.43  = { by axiom 3 (condensed_detachment) }
% 8.06/1.43    fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)))
% 8.06/1.43  = { by axiom 4 (lg_2) }
% 8.06/1.43    fresh2(true, true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(W, X), equivalent(W, Y)), Z)))
% 8.06/1.43  = { by axiom 1 (condensed_detachment) }
% 8.06/1.43    true
% 8.06/1.43  
% 8.06/1.43  Lemma 16: fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z))) = is_a_theorem(equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z))).
% 8.06/1.43  Proof:
% 8.06/1.43    fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z)))
% 8.06/1.43  = { by axiom 3 (condensed_detachment) R->L }
% 8.06/1.43    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z)))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z)))
% 8.06/1.43  = { by lemma 13 }
% 8.06/1.43    fresh(true, true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z)))
% 8.06/1.43  = { by axiom 2 (condensed_detachment) }
% 8.06/1.43    is_a_theorem(equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z)))
% 8.06/1.43  
% 8.06/1.43  Lemma 17: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, W)))), true, equivalent(Y, W)) = is_a_theorem(equivalent(Y, W)).
% 8.06/1.43  Proof:
% 8.06/1.43    fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, W)))), true, equivalent(Y, W))
% 8.06/1.43  = { by axiom 3 (condensed_detachment) R->L }
% 8.06/1.43    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, W))), equivalent(Y, W))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, W))), equivalent(Y, W))
% 8.06/1.43  = { by lemma 7 R->L }
% 8.06/1.43    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, W)), equivalent(X, W)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, W))), equivalent(Y, W)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, W))), equivalent(Y, W))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, W))), equivalent(Y, W))
% 8.06/1.43  = { by lemma 14 }
% 8.06/1.43    fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, W))), equivalent(Y, W))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, W))), equivalent(Y, W))
% 8.06/1.43  = { by axiom 1 (condensed_detachment) }
% 8.06/1.43    fresh(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, W))), equivalent(Y, W))
% 8.06/1.43  = { by axiom 2 (condensed_detachment) }
% 8.06/1.44    is_a_theorem(equivalent(Y, W))
% 8.06/1.44  
% 8.06/1.44  Goal 1 (prove_lg_1): is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)) = true.
% 8.06/1.44  Proof:
% 8.06/1.44    is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.06/1.44  = { by axiom 2 (condensed_detachment) R->L }
% 8.06/1.44    fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.06/1.44  = { by axiom 1 (condensed_detachment) R->L }
% 8.06/1.44    fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.06/1.44  = { by axiom 4 (lg_2) R->L }
% 8.06/1.44    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(a, equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.06/1.44  = { by axiom 3 (condensed_detachment) R->L }
% 8.06/1.44    fresh(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(a, equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(a, equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.06/1.44  = { by axiom 5 (lg_4) }
% 8.06/1.44    fresh(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(a, equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.06/1.44  = { by axiom 2 (condensed_detachment) }
% 8.06/1.44    fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.06/1.44  = { by axiom 3 (condensed_detachment) }
% 8.06/1.44    fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.06/1.44  = { by axiom 2 (condensed_detachment) R->L }
% 8.06/1.44    fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.06/1.44  = { by axiom 1 (condensed_detachment) R->L }
% 8.06/1.44    fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.06/1.44  = { by axiom 1 (condensed_detachment) R->L }
% 8.06/1.44    fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.06/1.44  = { by axiom 1 (condensed_detachment) R->L }
% 8.06/1.45    fresh2(fresh(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.06/1.45  = { by lemma 15 R->L }
% 8.06/1.45    fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), X), equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(b, b), a), X)), equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.06/1.45  = { by lemma 17 }
% 8.64/1.45    fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.64/1.45  = { by lemma 17 }
% 8.64/1.45    fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.64/1.45  = { by lemma 9 }
% 8.64/1.45    fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.64/1.45  = { by axiom 3 (condensed_detachment) }
% 8.64/1.45    fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.64/1.46  = { by axiom 2 (condensed_detachment) R->L }
% 8.64/1.46    fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.64/1.46  = { by axiom 1 (condensed_detachment) R->L }
% 8.64/1.46    fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.64/1.46  = { by axiom 4 (lg_2) R->L }
% 8.64/1.46    fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.64/1.46  = { by lemma 9 }
% 8.64/1.46    fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.64/1.46  = { by axiom 3 (condensed_detachment) }
% 8.64/1.46    fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.64/1.47  = { by lemma 17 R->L }
% 8.64/1.47    fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.64/1.47  = { by axiom 2 (condensed_detachment) R->L }
% 8.64/1.47    fresh2(fresh2(fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.64/1.47  = { by axiom 1 (condensed_detachment) R->L }
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% 8.64/1.48  = { by lemma 15 R->L }
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% 8.64/1.49  = { by lemma 7 }
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% 8.64/1.49  = { by axiom 3 (condensed_detachment) }
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% 8.64/1.50  = { by axiom 2 (condensed_detachment) R->L }
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% 8.64/1.51  = { by axiom 1 (condensed_detachment) R->L }
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% 8.64/1.52  = { by axiom 1 (condensed_detachment) R->L }
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% 8.64/1.53  = { by axiom 5 (lg_4) R->L }
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% 8.64/1.54  = { by lemma 11 }
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% 8.64/1.55  = { by axiom 3 (condensed_detachment) R->L }
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% 8.64/1.57  = { by axiom 2 (condensed_detachment) }
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% 8.64/1.58  = { by axiom 3 (condensed_detachment) }
% 8.64/1.58    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 8.64/1.59  = { by lemma 16 R->L }
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% 9.48/1.59  = { by lemma 16 R->L }
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% 9.48/1.60  = { by lemma 11 R->L }
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% 9.48/1.61  = { by lemma 8 }
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% 9.48/1.61  = { by axiom 1 (condensed_detachment) }
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% 9.48/1.62  = { by axiom 1 (condensed_detachment) }
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% 9.48/1.62  = { by axiom 1 (condensed_detachment) }
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% 9.48/1.62  = { by axiom 1 (condensed_detachment) }
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% 9.48/1.62  = { by axiom 1 (condensed_detachment) }
% 9.48/1.62    fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), a)), equivalent(equivalent(b, b), a)), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 9.48/1.62  = { by axiom 1 (condensed_detachment) }
% 9.48/1.62    fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 9.48/1.62  = { by axiom 1 (condensed_detachment) }
% 9.48/1.62    fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), a), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), a))), c), c)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 9.48/1.62  = { by axiom 1 (condensed_detachment) }
% 9.48/1.62    fresh2(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 9.48/1.62  = { by axiom 1 (condensed_detachment) }
% 9.48/1.62    true
% 9.48/1.62  % SZS output end Proof
% 9.48/1.62  
% 9.48/1.62  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------