%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL385-1 : TPTP v8.1.2. Released v2.3.0.
% 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 : n024.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 08:18:43 EDT 2023

% Result   : Unsatisfiable 251.98s 32.43s
% Output   : Proof 253.92s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL385-1 : TPTP v8.1.2. Released v2.3.0.
% 0.11/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34  % Computer : n024.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Fri Aug 25 03:07:09 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 251.98/32.43  Command-line arguments: --no-flatten-goal
% 251.98/32.43  
% 251.98/32.43  % SZS status Unsatisfiable
% 251.98/32.44  
% 253.13/32.53  % SZS output start Proof
% 253.13/32.53  Take the following subset of the input axioms:
% 253.13/32.53    fof(cn_1, axiom, ![X, Y, Z]: is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))).
% 253.13/32.53    fof(cn_2, axiom, ![X2]: is_a_theorem(implies(implies(not(X2), X2), X2))).
% 253.13/32.53    fof(cn_3, axiom, ![X2, Y2]: is_a_theorem(implies(X2, implies(not(X2), Y2)))).
% 253.13/32.53    fof(condensed_detachment, axiom, ![X2, Y2]: (~is_a_theorem(implies(X2, Y2)) | (~is_a_theorem(X2) | is_a_theorem(Y2)))).
% 253.13/32.53    fof(prove_cn_47, negated_conjecture, ~is_a_theorem(implies(implies(x, not(y)), implies(y, not(x))))).
% 253.13/32.53  
% 253.13/32.53  Now clausify the problem and encode Horn clauses using encoding 3 of
% 253.13/32.53  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 253.13/32.53  We repeatedly replace C & s=t => u=v by the two clauses:
% 253.13/32.53    fresh(y, y, x1...xn) = u
% 253.13/32.53    C => fresh(s, t, x1...xn) = v
% 253.13/32.53  where fresh is a fresh function symbol and x1..xn are the free
% 253.13/32.53  variables of u and v.
% 253.13/32.53  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 253.13/32.53  input problem has no model of domain size 1).
% 253.13/32.53  
% 253.13/32.53  The encoding turns the above axioms into the following unit equations and goals:
% 253.13/32.53  
% 253.13/32.53  Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 253.13/32.53  Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 253.13/32.53  Axiom 3 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 253.13/32.53  Axiom 4 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 253.13/32.53  Axiom 5 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 253.13/32.53  Axiom 6 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 253.13/32.53  
% 253.13/32.53  Lemma 7: fresh2(is_a_theorem(implies(not(X), X)), true, X) = is_a_theorem(X).
% 253.13/32.53  Proof:
% 253.13/32.53    fresh2(is_a_theorem(implies(not(X), X)), true, X)
% 253.13/32.53  = { by axiom 5 (condensed_detachment) R->L }
% 253.13/32.53    fresh(is_a_theorem(implies(implies(not(X), X), X)), true, implies(not(X), X), X)
% 253.13/32.53  = { by axiom 4 (cn_2) }
% 253.13/32.53    fresh(true, true, implies(not(X), X), X)
% 253.13/32.53  = { by axiom 2 (condensed_detachment) }
% 253.13/32.53    is_a_theorem(X)
% 253.13/32.53  
% 253.13/32.53  Lemma 8: fresh2(is_a_theorem(implies(X, Y)), true, implies(implies(Y, Z), implies(X, Z))) = is_a_theorem(implies(implies(Y, Z), implies(X, Z))).
% 253.13/32.53  Proof:
% 253.13/32.53    fresh2(is_a_theorem(implies(X, Y)), true, implies(implies(Y, Z), implies(X, Z)))
% 253.13/32.53  = { by axiom 5 (condensed_detachment) R->L }
% 253.13/32.53    fresh(is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))), true, implies(X, Y), implies(implies(Y, Z), implies(X, Z)))
% 253.13/32.53  = { by axiom 6 (cn_1) }
% 253.13/32.53    fresh(true, true, implies(X, Y), implies(implies(Y, Z), implies(X, Z)))
% 253.13/32.53  = { by axiom 2 (condensed_detachment) }
% 253.13/32.53    is_a_theorem(implies(implies(Y, Z), implies(X, Z)))
% 253.13/32.53  
% 253.13/32.53  Lemma 9: is_a_theorem(implies(implies(X, Y), implies(implies(not(X), X), Y))) = true.
% 253.13/32.53  Proof:
% 253.13/32.53    is_a_theorem(implies(implies(X, Y), implies(implies(not(X), X), Y)))
% 253.13/32.53  = { by lemma 8 R->L }
% 253.13/32.53    fresh2(is_a_theorem(implies(implies(not(X), X), X)), true, implies(implies(X, Y), implies(implies(not(X), X), Y)))
% 253.13/32.53  = { by axiom 4 (cn_2) }
% 253.13/32.53    fresh2(true, true, implies(implies(X, Y), implies(implies(not(X), X), Y)))
% 253.13/32.53  = { by axiom 1 (condensed_detachment) }
% 253.13/32.53    true
% 253.13/32.53  
% 253.13/32.53  Lemma 10: is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))) = true.
% 253.13/32.53  Proof:
% 253.13/32.53    is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W)))
% 253.13/32.53  = { by lemma 8 R->L }
% 253.13/32.53    fresh2(is_a_theorem(implies(implies(Z, X), implies(implies(X, Y), implies(Z, Y)))), true, implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W)))
% 253.13/32.53  = { by axiom 6 (cn_1) }
% 253.13/32.53    fresh2(true, true, implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W)))
% 253.13/32.53  = { by axiom 1 (condensed_detachment) }
% 253.13/32.53    true
% 253.13/32.53  
% 253.13/32.53  Lemma 11: fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, implies(implies(Z, X), W)) = is_a_theorem(implies(implies(Z, X), W)).
% 253.13/32.53  Proof:
% 253.13/32.53    fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, implies(implies(Z, X), W))
% 253.13/32.53  = { by axiom 5 (condensed_detachment) R->L }
% 253.13/32.53    fresh(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))), true, implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))
% 253.13/32.53  = { by lemma 10 }
% 253.13/32.53    fresh(true, true, implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))
% 253.13/32.53  = { by axiom 2 (condensed_detachment) }
% 253.13/32.53    is_a_theorem(implies(implies(Z, X), W))
% 253.13/32.53  
% 253.13/32.53  Lemma 12: is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z))) = true.
% 253.13/32.53  Proof:
% 253.13/32.53    is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 253.13/32.53  = { by lemma 8 R->L }
% 253.13/32.53    fresh2(is_a_theorem(implies(X, implies(not(X), Y))), true, implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 253.13/32.53  = { by axiom 3 (cn_3) }
% 253.13/32.53    fresh2(true, true, implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 253.13/32.53  = { by axiom 1 (condensed_detachment) }
% 253.13/32.53    true
% 253.13/32.53  
% 253.13/32.53  Lemma 13: is_a_theorem(implies(implies(X, not(Y)), implies(Y, implies(X, Z)))) = true.
% 253.13/32.53  Proof:
% 253.13/32.53    is_a_theorem(implies(implies(X, not(Y)), implies(Y, implies(X, Z))))
% 253.13/32.53  = { by lemma 11 R->L }
% 253.13/32.53    fresh2(is_a_theorem(implies(implies(implies(not(Y), Z), implies(X, Z)), implies(Y, implies(X, Z)))), true, implies(implies(X, not(Y)), implies(Y, implies(X, Z))))
% 253.13/32.53  = { by lemma 12 }
% 253.13/32.53    fresh2(true, true, implies(implies(X, not(Y)), implies(Y, implies(X, Z))))
% 253.13/32.53  = { by axiom 1 (condensed_detachment) }
% 253.13/32.53    true
% 253.13/32.53  
% 253.13/32.53  Lemma 14: fresh2(is_a_theorem(implies(implies(not(X), Y), Z)), true, implies(X, Z)) = is_a_theorem(implies(X, Z)).
% 253.13/32.54  Proof:
% 253.13/32.54    fresh2(is_a_theorem(implies(implies(not(X), Y), Z)), true, implies(X, Z))
% 253.13/32.54  = { by axiom 5 (condensed_detachment) R->L }
% 253.13/32.54    fresh(is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z))), true, implies(implies(not(X), Y), Z), implies(X, Z))
% 253.13/32.54  = { by lemma 12 }
% 253.13/32.54    fresh(true, true, implies(implies(not(X), Y), Z), implies(X, Z))
% 253.13/32.54  = { by axiom 2 (condensed_detachment) }
% 253.13/32.54    is_a_theorem(implies(X, Z))
% 253.13/32.54  
% 253.13/32.54  Lemma 15: fresh2(is_a_theorem(implies(implies(implies(not(X), X), Y), Z)), true, implies(implies(X, Y), Z)) = is_a_theorem(implies(implies(X, Y), Z)).
% 253.13/32.54  Proof:
% 253.13/32.54    fresh2(is_a_theorem(implies(implies(implies(not(X), X), Y), Z)), true, implies(implies(X, Y), Z))
% 253.13/32.54  = { by axiom 5 (condensed_detachment) R->L }
% 253.13/32.54    fresh(is_a_theorem(implies(implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))), true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 253.13/32.54  = { by lemma 8 R->L }
% 253.13/32.54    fresh(fresh2(is_a_theorem(implies(implies(X, Y), implies(implies(not(X), X), Y))), true, implies(implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))), true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 253.13/32.54  = { by lemma 9 }
% 253.13/32.54    fresh(fresh2(true, true, implies(implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))), true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 253.13/32.54  = { by axiom 1 (condensed_detachment) }
% 253.13/32.54    fresh(true, true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 253.13/32.54  = { by axiom 2 (condensed_detachment) }
% 253.13/32.54    is_a_theorem(implies(implies(X, Y), Z))
% 253.13/32.54  
% 253.13/32.54  Lemma 16: is_a_theorem(implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y))) = true.
% 253.13/32.54  Proof:
% 253.13/32.54    is_a_theorem(implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 253.13/32.54  = { by lemma 15 R->L }
% 253.13/32.54    fresh2(is_a_theorem(implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 253.13/32.54  = { by lemma 8 R->L }
% 253.29/32.54    fresh2(fresh2(is_a_theorem(implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 253.29/32.54  = { by lemma 14 R->L }
% 253.29/32.54    fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 253.29/32.54  = { by lemma 8 R->L }
% 253.29/32.54    fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(not(X), X), X)), not(Z))), true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 253.29/32.54  = { by axiom 2 (condensed_detachment) R->L }
% 253.29/32.54    fresh2(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(not(X), X), X), implies(not(implies(implies(not(X), X), X)), not(Z))), true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 253.29/32.54  = { by axiom 3 (cn_3) R->L }
% 253.29/32.54    fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(not(X), X), X), implies(not(implies(implies(not(X), X), X)), not(Z)))), true, implies(implies(not(X), X), X), implies(not(implies(implies(not(X), X), X)), not(Z))), true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 253.29/32.54  = { by axiom 5 (condensed_detachment) }
% 253.29/32.54    fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(X), X), X)), true, implies(not(implies(implies(not(X), X), X)), not(Z))), true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 253.29/32.54  = { by axiom 4 (cn_2) }
% 253.29/32.54    fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(not(X), X), X)), not(Z))), true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 253.29/32.54  = { by axiom 1 (condensed_detachment) }
% 253.29/32.54    fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 253.29/32.54  = { by axiom 1 (condensed_detachment) }
% 253.29/32.54    fresh2(fresh2(fresh2(true, true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 253.29/32.54  = { by axiom 1 (condensed_detachment) }
% 253.29/32.54    fresh2(fresh2(true, true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 253.29/32.54  = { by axiom 1 (condensed_detachment) }
% 253.29/32.54    fresh2(true, true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 253.29/32.54  = { by axiom 1 (condensed_detachment) }
% 253.29/32.54    true
% 253.29/32.54  
% 253.29/32.54  Lemma 17: is_a_theorem(implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))) = true.
% 253.29/32.54  Proof:
% 253.29/32.54    is_a_theorem(implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y))))
% 253.29/32.54  = { by lemma 11 R->L }
% 253.29/32.54    fresh2(is_a_theorem(implies(implies(implies(implies(not(Y), Y), Y), implies(X, Y)), implies(Z, implies(X, Y)))), true, implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y))))
% 253.29/32.54  = { by lemma 16 }
% 253.29/32.54    fresh2(true, true, implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y))))
% 253.29/32.54  = { by axiom 1 (condensed_detachment) }
% 253.29/32.54    true
% 253.29/32.54  
% 253.29/32.54  Lemma 18: fresh2(is_a_theorem(implies(X, implies(not(Y), Y))), true, implies(Z, implies(X, Y))) = is_a_theorem(implies(Z, implies(X, Y))).
% 253.29/32.54  Proof:
% 253.29/32.54    fresh2(is_a_theorem(implies(X, implies(not(Y), Y))), true, implies(Z, implies(X, Y)))
% 253.29/32.54  = { by axiom 5 (condensed_detachment) R->L }
% 253.29/32.54    fresh(is_a_theorem(implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 253.29/32.54  = { by lemma 17 }
% 253.29/32.54    fresh(true, true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 253.29/32.54  = { by axiom 2 (condensed_detachment) }
% 253.29/32.54    is_a_theorem(implies(Z, implies(X, Y)))
% 253.29/32.54  
% 253.29/32.54  Lemma 19: fresh2(is_a_theorem(implies(implies(X, implies(not(Y), Z)), W)), true, implies(Y, W)) = is_a_theorem(implies(Y, W)).
% 253.29/32.54  Proof:
% 253.29/32.54    fresh2(is_a_theorem(implies(implies(X, implies(not(Y), Z)), W)), true, implies(Y, W))
% 253.29/32.54  = { by axiom 5 (condensed_detachment) R->L }
% 253.29/32.54    fresh(is_a_theorem(implies(implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))), true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 253.29/32.54  = { by lemma 8 R->L }
% 253.29/32.54    fresh(fresh2(is_a_theorem(implies(Y, implies(X, implies(not(Y), Z)))), true, implies(implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))), true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 253.29/32.54  = { by lemma 14 R->L }
% 253.29/32.54    fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(Y), not(X)), implies(X, implies(not(Y), Z)))), true, implies(Y, implies(X, implies(not(Y), Z)))), true, implies(implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))), true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 253.29/32.54  = { by lemma 13 }
% 253.29/32.54    fresh(fresh2(fresh2(true, true, implies(Y, implies(X, implies(not(Y), Z)))), true, implies(implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))), true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 253.29/32.54  = { by axiom 1 (condensed_detachment) }
% 253.29/32.54    fresh(fresh2(true, true, implies(implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))), true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 253.29/32.54  = { by axiom 1 (condensed_detachment) }
% 253.29/32.54    fresh(true, true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 253.29/32.54  = { by axiom 2 (condensed_detachment) }
% 253.29/32.54    is_a_theorem(implies(Y, W))
% 253.29/32.54  
% 253.29/32.54  Lemma 20: is_a_theorem(implies(implies(implies(implies(not(not(X)), not(X)), Y), Z), implies(X, Z))) = true.
% 253.29/32.54  Proof:
% 253.29/32.54    is_a_theorem(implies(implies(implies(implies(not(not(X)), not(X)), Y), Z), implies(X, Z)))
% 253.29/32.54  = { by lemma 8 R->L }
% 253.29/32.54    fresh2(is_a_theorem(implies(X, implies(implies(not(not(X)), not(X)), Y))), true, implies(implies(implies(implies(not(not(X)), not(X)), Y), Z), implies(X, Z)))
% 253.29/32.54  = { by lemma 14 R->L }
% 253.29/32.54    fresh2(fresh2(is_a_theorem(implies(implies(not(X), Y), implies(implies(not(not(X)), not(X)), Y))), true, implies(X, implies(implies(not(not(X)), not(X)), Y))), true, implies(implies(implies(implies(not(not(X)), not(X)), Y), Z), implies(X, Z)))
% 253.29/32.54  = { by lemma 9 }
% 253.29/32.54    fresh2(fresh2(true, true, implies(X, implies(implies(not(not(X)), not(X)), Y))), true, implies(implies(implies(implies(not(not(X)), not(X)), Y), Z), implies(X, Z)))
% 253.29/32.54  = { by axiom 1 (condensed_detachment) }
% 253.29/32.54    fresh2(true, true, implies(implies(implies(implies(not(not(X)), not(X)), Y), Z), implies(X, Z)))
% 253.29/32.54  = { by axiom 1 (condensed_detachment) }
% 253.29/32.55    true
% 253.29/32.55  
% 253.29/32.55  Goal 1 (prove_cn_47): is_a_theorem(implies(implies(x, not(y)), implies(y, not(x)))) = true.
% 253.29/32.55  Proof:
% 253.29/32.55    is_a_theorem(implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.55  = { by lemma 15 R->L }
% 253.29/32.55    fresh2(is_a_theorem(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.55  = { by axiom 2 (condensed_detachment) R->L }
% 253.29/32.55    fresh2(fresh(true, true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.55  = { by axiom 1 (condensed_detachment) R->L }
% 253.29/32.55    fresh2(fresh(fresh2(true, true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.55  = { by axiom 1 (condensed_detachment) R->L }
% 253.29/32.55    fresh2(fresh(fresh2(fresh2(true, true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.55  = { by axiom 1 (condensed_detachment) R->L }
% 253.29/32.55    fresh2(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.55  = { by axiom 1 (condensed_detachment) R->L }
% 253.29/32.55    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.55  = { by axiom 1 (condensed_detachment) R->L }
% 253.29/32.55    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.56  = { by axiom 1 (condensed_detachment) R->L }
% 253.29/32.56    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.56  = { by axiom 1 (condensed_detachment) R->L }
% 253.29/32.56    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.56  = { by axiom 1 (condensed_detachment) R->L }
% 253.29/32.56    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), implies(not(not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(not(implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.56  = { by axiom 1 (condensed_detachment) R->L }
% 253.29/32.56    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(not(implies(not(not(not(x))), not(not(x))))), implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), implies(not(not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(not(implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.57  = { by axiom 1 (condensed_detachment) R->L }
% 253.29/32.57    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(not(not(not(x))), implies(not(not(not(implies(not(not(not(x))), not(not(x)))))), not(not(implies(not(not(not(x))), not(not(x))))))), implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))))), true, implies(not(not(implies(not(not(not(x))), not(not(x))))), implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), implies(not(not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(not(implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.57  = { by lemma 20 R->L }
% 253.29/32.57    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(not(x))), not(not(x)))))), not(not(implies(not(not(not(x))), not(not(x)))))), not(not(x))), implies(not(not(not(x))), not(not(x)))), implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), implies(not(not(not(implies(not(not(not(x))), not(not(x)))))), not(not(implies(not(not(not(x))), not(not(x))))))), implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))))), true, implies(not(not(implies(not(not(not(x))), not(not(x))))), implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), implies(not(not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(not(implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.57  = { by lemma 11 }
% 253.29/32.57    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(not(not(x))), implies(not(not(not(implies(not(not(not(x))), not(not(x)))))), not(not(implies(not(not(not(x))), not(not(x))))))), implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))))), true, implies(not(not(implies(not(not(not(x))), not(not(x))))), implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), implies(not(not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(not(implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.57  = { by lemma 19 }
% 253.29/32.57    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(not(implies(not(not(not(x))), not(not(x))))), implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), implies(not(not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(not(implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.57  = { by lemma 8 }
% 253.29/32.57    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), implies(not(not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(not(implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.58  = { by lemma 18 }
% 253.29/32.58    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))))), true, implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.58  = { by lemma 7 }
% 253.29/32.58    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(implies(not(not(not(x))), not(not(x)))), implies(not(not(not(x))), not(not(x)))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.58  = { by lemma 15 }
% 253.29/32.58    fresh2(fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x)))))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.58  = { by axiom 5 (condensed_detachment) R->L }
% 253.29/32.58    fresh2(fresh(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))), implies(not(x), not(implies(not(not(not(x))), not(not(x))))))), true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))), implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.58  = { by lemma 20 }
% 253.29/32.58    fresh2(fresh(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(not(not(not(x))), not(not(x))), not(implies(not(not(not(x))), not(not(x))))), not(implies(not(not(not(x))), not(not(x))))), implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.58  = { by axiom 2 (condensed_detachment) }
% 253.29/32.58    fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(not(x), not(implies(not(not(not(x))), not(not(x)))))), true, implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.58  = { by axiom 5 (condensed_detachment) R->L }
% 253.29/32.58    fresh2(fresh(fresh2(fresh2(fresh(is_a_theorem(implies(implies(not(x), not(implies(not(not(not(x))), not(not(x))))), implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x)))), true, implies(not(x), not(implies(not(not(not(x))), not(not(x))))), implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.58  = { by lemma 13 }
% 253.29/32.58    fresh2(fresh(fresh2(fresh2(fresh(true, true, implies(not(x), not(implies(not(not(not(x))), not(not(x))))), implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.58  = { by axiom 2 (condensed_detachment) }
% 253.29/32.58    fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(not(not(x))), not(not(x))), implies(not(x), x))), true, implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.58  = { by lemma 14 }
% 253.29/32.58    fresh2(fresh(fresh2(is_a_theorem(implies(not(not(x)), implies(not(x), x))), true, implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.58  = { by axiom 5 (condensed_detachment) R->L }
% 253.29/32.58    fresh2(fresh(fresh(is_a_theorem(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.58  = { by lemma 7 R->L }
% 253.29/32.58    fresh2(fresh(fresh(fresh2(is_a_theorem(implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.59  = { by lemma 18 R->L }
% 253.29/32.59    fresh2(fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.59  = { by axiom 2 (condensed_detachment) R->L }
% 253.29/32.59    fresh2(fresh(fresh(fresh2(fresh2(fresh(true, true, implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.59  = { by axiom 1 (condensed_detachment) R->L }
% 253.29/32.60    fresh2(fresh(fresh(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))))), true, implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.60  = { by axiom 1 (condensed_detachment) R->L }
% 253.29/32.60    fresh2(fresh(fresh(fresh2(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(not(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))))), true, implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))))), true, implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.61  = { by axiom 1 (condensed_detachment) R->L }
% 253.29/32.61    fresh2(fresh(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))))), true, implies(implies(implies(not(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))))), true, implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))))), true, implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.29/32.61  = { by lemma 17 R->L }
% 253.92/32.62    fresh2(fresh(fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(implies(not(not(x)), implies(not(x), x))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))))), true, implies(implies(implies(not(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))))), true, implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))))), true, implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.62  = { by lemma 19 }
% 253.92/32.62    fresh2(fresh(fresh(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))))), true, implies(implies(implies(not(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))))), true, implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))))), true, implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.62  = { by lemma 8 }
% 253.92/32.63    fresh2(fresh(fresh(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(not(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x)))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))))), true, implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))))), true, implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.63  = { by lemma 15 }
% 253.92/32.63    fresh2(fresh(fresh(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))))), true, implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.63  = { by axiom 5 (condensed_detachment) }
% 253.92/32.63    fresh2(fresh(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.63  = { by lemma 11 R->L }
% 253.92/32.63    fresh2(fresh(fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.64  = { by lemma 17 }
% 253.92/32.64    fresh2(fresh(fresh(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(not(x)), implies(not(x), x))), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.64  = { by axiom 1 (condensed_detachment) }
% 253.92/32.64    fresh2(fresh(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(not(not(x)), implies(not(x), x)), implies(not(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.64  = { by axiom 1 (condensed_detachment) }
% 253.92/32.64    fresh2(fresh(fresh(fresh2(fresh2(true, true, implies(not(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.64  = { by axiom 1 (condensed_detachment) }
% 253.92/32.64    fresh2(fresh(fresh(fresh2(true, true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.64  = { by axiom 1 (condensed_detachment) }
% 253.92/32.64    fresh2(fresh(fresh(true, true, implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.64  = { by axiom 2 (condensed_detachment) }
% 253.92/32.64    fresh2(fresh(is_a_theorem(implies(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.64  = { by axiom 5 (condensed_detachment) }
% 253.92/32.64    fresh2(fresh2(is_a_theorem(implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.64  = { by lemma 11 R->L }
% 253.92/32.64    fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.64  = { by axiom 2 (condensed_detachment) R->L }
% 253.92/32.64    fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.64  = { by axiom 1 (condensed_detachment) R->L }
% 253.92/32.64    fresh2(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.65  = { by axiom 1 (condensed_detachment) R->L }
% 253.92/32.65    fresh2(fresh2(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.65  = { by axiom 1 (condensed_detachment) R->L }
% 253.92/32.65    fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.65  = { by lemma 16 R->L }
% 253.92/32.65    fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(not(implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.65  = { by lemma 18 }
% 253.92/32.65    fresh2(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), implies(implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.65  = { by lemma 7 }
% 253.92/32.66    fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.66  = { by lemma 11 }
% 253.92/32.66    fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.66  = { by axiom 5 (condensed_detachment) }
% 253.92/32.66    fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.66  = { by axiom 2 (condensed_detachment) R->L }
% 253.92/32.66    fresh2(fresh2(fresh2(fresh2(fresh(true, true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.66  = { by axiom 1 (condensed_detachment) R->L }
% 253.92/32.66    fresh2(fresh2(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.66  = { by lemma 10 R->L }
% 253.92/32.66    fresh2(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(not(not(x)), not(y)), implies(y, not(x))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.66  = { by lemma 11 }
% 253.92/32.66    fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))))), true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x)))), implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.66  = { by axiom 5 (condensed_detachment) }
% 253.92/32.66    fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.66  = { by lemma 18 R->L }
% 253.92/32.66    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(not(x)), not(y)), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by lemma 11 R->L }
% 253.92/32.67    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(y), not(x)), implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(implies(not(not(x)), not(y)), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by axiom 2 (condensed_detachment) R->L }
% 253.92/32.67    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(y, implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x)))), implies(implies(implies(not(y), not(x)), implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(implies(not(not(x)), not(y)), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by axiom 1 (condensed_detachment) R->L }
% 253.92/32.67    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(y, implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x)))), implies(implies(implies(not(y), not(x)), implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x)))))), true, implies(implies(y, implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x)))), implies(implies(implies(not(y), not(x)), implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(implies(not(not(x)), not(y)), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by lemma 12 R->L }
% 253.92/32.67    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(not(y), not(x)), implies(not(not(x)), not(x))), implies(y, implies(not(not(x)), not(x))))), true, implies(implies(implies(y, implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x)))), implies(implies(implies(not(y), not(x)), implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x)))))), true, implies(implies(y, implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x)))), implies(implies(implies(not(y), not(x)), implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(implies(not(not(x)), not(y)), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by lemma 8 }
% 253.92/32.67    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(y, implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x)))), implies(implies(implies(not(y), not(x)), implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x)))))), true, implies(implies(y, implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x)))), implies(implies(implies(not(y), not(x)), implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(implies(not(not(x)), not(y)), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by axiom 5 (condensed_detachment) }
% 253.92/32.67    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(y, implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(implies(implies(not(y), not(x)), implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(implies(not(not(x)), not(y)), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by lemma 17 }
% 253.92/32.67    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(not(y), not(x)), implies(not(not(x)), not(x))), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(implies(not(not(x)), not(y)), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by axiom 1 (condensed_detachment) }
% 253.92/32.67    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(not(not(x)), not(y)), implies(not(implies(y, not(x))), implies(y, not(x))))), true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by axiom 1 (condensed_detachment) }
% 253.92/32.67    fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(not(not(x)), not(y)), implies(y, not(x))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by axiom 1 (condensed_detachment) }
% 253.92/32.67    fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(not(implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))))), true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by axiom 1 (condensed_detachment) }
% 253.92/32.67    fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(not(x), x), not(y)), implies(not(not(x)), not(y))), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by axiom 1 (condensed_detachment) }
% 253.92/32.67    fresh2(fresh2(fresh2(true, true, implies(implies(not(not(x)), implies(not(x), x)), implies(implies(implies(not(x), x), not(y)), implies(y, not(x))))), true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by axiom 1 (condensed_detachment) }
% 253.92/32.67    fresh2(fresh2(true, true, implies(implies(implies(not(x), x), not(y)), implies(y, not(x)))), true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by axiom 1 (condensed_detachment) }
% 253.92/32.67    fresh2(true, true, implies(implies(x, not(y)), implies(y, not(x))))
% 253.92/32.67  = { by axiom 1 (condensed_detachment) }
% 253.92/32.67    true
% 253.92/32.67  % SZS output end Proof
% 253.92/32.67  
% 253.92/32.67  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------