%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL103-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 08:17:26 EDT 2023

% Result   : Unsatisfiable 90.82s 12.31s
% Output   : Proof 93.60s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : LCL103-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.15  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.36  % Computer : n012.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Thu Aug 24 21:40:26 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 90.82/12.31  Command-line arguments: --no-flatten-goal
% 90.82/12.31  
% 90.82/12.31  % SZS status Unsatisfiable
% 90.82/12.31  
% 92.81/12.35  % SZS output start Proof
% 92.81/12.35  Take the following subset of the input axioms:
% 92.81/12.35    fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 92.81/12.35    fof(p_1, axiom, ![Z, U, X2, Y2]: is_a_theorem(equivalent(equivalent(equivalent(X2, Y2), Z), equivalent(equivalent(U, Y2), equivalent(equivalent(X2, U), Z))))).
% 92.81/12.35    fof(prove_lg_2, negated_conjecture, ~is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))).
% 92.81/12.35    fof(q_3, axiom, ![X2, Y2, Z2]: is_a_theorem(equivalent(equivalent(equivalent(X2, Y2), equivalent(equivalent(Y2, X2), Z2)), Z2))).
% 92.81/12.35  
% 92.81/12.35  Now clausify the problem and encode Horn clauses using encoding 3 of
% 92.81/12.35  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 92.81/12.35  We repeatedly replace C & s=t => u=v by the two clauses:
% 92.81/12.35    fresh(y, y, x1...xn) = u
% 92.81/12.35    C => fresh(s, t, x1...xn) = v
% 92.81/12.35  where fresh is a fresh function symbol and x1..xn are the free
% 92.81/12.35  variables of u and v.
% 92.81/12.35  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 92.81/12.35  input problem has no model of domain size 1).
% 92.81/12.35  
% 92.81/12.35  The encoding turns the above axioms into the following unit equations and goals:
% 92.81/12.35  
% 92.81/12.35  Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 92.81/12.35  Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 92.81/12.35  Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 92.81/12.35  Axiom 4 (q_3): is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, X), Z)), Z)) = true.
% 92.81/12.35  Axiom 5 (p_1): is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z)))) = true.
% 92.81/12.35  
% 92.81/12.35  Lemma 6: fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z))) = is_a_theorem(equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z))).
% 92.81/12.35  Proof:
% 92.81/12.35    fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z)))
% 92.81/12.35  = { by axiom 3 (condensed_detachment) R->L }
% 92.81/12.35    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z)))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z)))
% 92.81/12.35  = { by axiom 5 (p_1) }
% 92.81/12.36    fresh(true, true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z)))
% 92.81/12.36  = { by axiom 2 (condensed_detachment) }
% 92.81/12.36    is_a_theorem(equivalent(equivalent(W, Y), equivalent(equivalent(X, W), Z)))
% 92.81/12.36  
% 92.81/12.36  Lemma 7: is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(Z, Y), X), W))) = true.
% 92.81/12.36  Proof:
% 92.81/12.36    is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(Z, Y), X), W)))
% 92.81/12.36  = { by lemma 6 R->L }
% 92.81/12.36    fresh2(is_a_theorem(equivalent(equivalent(equivalent(Z, Y), equivalent(equivalent(Y, Z), W)), W)), true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(Z, Y), X), W)))
% 92.81/12.36  = { by axiom 4 (q_3) }
% 92.81/12.36    fresh2(true, true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(Z, Y), X), W)))
% 92.81/12.36  = { by axiom 1 (condensed_detachment) }
% 92.81/12.36    true
% 92.81/12.36  
% 92.81/12.36  Lemma 8: fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), W))), true, equivalent(equivalent(equivalent(Z, Y), X), W)) = is_a_theorem(equivalent(equivalent(equivalent(Z, Y), X), W)).
% 92.81/12.36  Proof:
% 92.81/12.36    fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), W))), true, equivalent(equivalent(equivalent(Z, Y), X), W))
% 92.81/12.36  = { by axiom 3 (condensed_detachment) R->L }
% 92.81/12.36    fresh(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(Z, Y), X), W))), true, equivalent(X, equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(Z, Y), X), W))
% 92.81/12.36  = { by lemma 7 }
% 92.81/12.36    fresh(true, true, equivalent(X, equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(Z, Y), X), W))
% 92.81/12.36  = { by axiom 2 (condensed_detachment) }
% 92.81/12.36    is_a_theorem(equivalent(equivalent(equivalent(Z, Y), X), W))
% 92.81/12.36  
% 92.81/12.36  Lemma 9: is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(equivalent(Z, Y), W))), W)) = true.
% 92.81/12.36  Proof:
% 92.81/12.36    is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(equivalent(Z, Y), W))), W))
% 92.81/12.36  = { by lemma 8 R->L }
% 92.81/12.36    fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Z, Y), W)), equivalent(equivalent(equivalent(Y, Z), X), W))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(equivalent(Z, Y), W))), W))
% 92.81/12.36  = { by lemma 7 }
% 92.81/12.36    fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(equivalent(Z, Y), W))), W))
% 92.81/12.36  = { by axiom 1 (condensed_detachment) }
% 92.81/12.36    true
% 92.81/12.36  
% 92.81/12.36  Lemma 10: is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y)))) = true.
% 92.81/12.36  Proof:
% 92.81/12.36    is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 92.81/12.36  = { by lemma 6 R->L }
% 92.81/12.36    fresh2(is_a_theorem(equivalent(equivalent(Z, Y), equivalent(Z, Y))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 92.81/12.36  = { by axiom 2 (condensed_detachment) R->L }
% 92.81/12.36    fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(Z, Y), W), equivalent(equivalent(Z, Y), equivalent(Z, Y))), equivalent(equivalent(equivalent(Z, Y), W), equivalent(equivalent(equivalent(Z, Y), equivalent(Z, Y)), equivalent(equivalent(Z, Y), equivalent(Z, Y))))), equivalent(equivalent(Z, Y), equivalent(Z, Y))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 92.81/12.36  = { by lemma 9 R->L }
% 92.81/12.36    fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z, Y), W), equivalent(equivalent(Z, Y), equivalent(Z, Y))), equivalent(equivalent(equivalent(Z, Y), W), equivalent(equivalent(equivalent(Z, Y), equivalent(Z, Y)), equivalent(equivalent(Z, Y), equivalent(Z, Y))))), equivalent(equivalent(Z, Y), equivalent(Z, Y)))), true, equivalent(equivalent(equivalent(equivalent(Z, Y), W), equivalent(equivalent(Z, Y), equivalent(Z, Y))), equivalent(equivalent(equivalent(Z, Y), W), equivalent(equivalent(equivalent(Z, Y), equivalent(Z, Y)), equivalent(equivalent(Z, Y), equivalent(Z, Y))))), equivalent(equivalent(Z, Y), equivalent(Z, Y))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 92.81/12.36  = { by axiom 3 (condensed_detachment) }
% 92.81/12.36    fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z, Y), W), equivalent(equivalent(Z, Y), equivalent(Z, Y))), equivalent(equivalent(equivalent(Z, Y), W), equivalent(equivalent(equivalent(Z, Y), equivalent(Z, Y)), equivalent(equivalent(Z, Y), equivalent(Z, Y)))))), true, equivalent(equivalent(Z, Y), equivalent(Z, Y))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 92.81/12.36  = { by axiom 5 (p_1) }
% 92.81/12.36    fresh2(fresh2(true, true, equivalent(equivalent(Z, Y), equivalent(Z, Y))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 92.81/12.36  = { by axiom 1 (condensed_detachment) }
% 92.81/12.36    fresh2(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 92.81/12.36  = { by axiom 1 (condensed_detachment) }
% 92.81/12.36    true
% 92.81/12.36  
% 92.81/12.36  Lemma 11: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))) = true.
% 92.81/12.36  Proof:
% 92.81/12.36    is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)))
% 92.81/12.36  = { by lemma 8 R->L }
% 92.81/12.36    fresh2(is_a_theorem(equivalent(equivalent(X, Z), equivalent(equivalent(Y, X), equivalent(Y, Z)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)))
% 92.81/12.36  = { by lemma 10 }
% 92.81/12.36    fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)))
% 92.81/12.36  = { by axiom 1 (condensed_detachment) }
% 92.81/12.36    true
% 92.81/12.36  
% 92.81/12.36  Lemma 12: fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(Z, X), equivalent(Z, Y))) = is_a_theorem(equivalent(equivalent(Z, X), equivalent(Z, Y))).
% 92.81/12.36  Proof:
% 92.81/12.36    fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(Z, X), equivalent(Z, Y)))
% 92.81/12.36  = { by axiom 3 (condensed_detachment) R->L }
% 92.81/12.36    fresh(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y)))), true, equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y)))
% 92.81/12.36  = { by lemma 10 }
% 92.81/12.36    fresh(true, true, equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y)))
% 92.81/12.36  = { by axiom 2 (condensed_detachment) }
% 92.81/12.36    is_a_theorem(equivalent(equivalent(Z, X), equivalent(Z, Y)))
% 92.81/12.36  
% 92.81/12.36  Lemma 13: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, equivalent(Y, Z)) = is_a_theorem(equivalent(Y, Z)).
% 92.81/12.36  Proof:
% 92.81/12.36    fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, equivalent(Y, Z))
% 92.81/12.36  = { by axiom 3 (condensed_detachment) R->L }
% 92.81/12.36    fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))), true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))
% 92.81/12.36  = { by lemma 11 }
% 92.81/12.36    fresh(true, true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))
% 92.81/12.36  = { by axiom 2 (condensed_detachment) }
% 92.81/12.36    is_a_theorem(equivalent(Y, Z))
% 92.81/12.36  
% 92.81/12.36  Goal 1 (prove_lg_2): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e)) = true.
% 92.81/12.36  Proof:
% 92.81/12.36    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.36  = { by axiom 2 (condensed_detachment) R->L }
% 92.81/12.36    fresh(true, true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.36  = { by axiom 1 (condensed_detachment) R->L }
% 92.81/12.36    fresh(fresh2(true, true, equivalent(equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.36  = { by lemma 9 R->L }
% 92.81/12.36    fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), e)), true, equivalent(equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.36  = { by lemma 6 }
% 92.81/12.36    fresh(is_a_theorem(equivalent(equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.36  = { by axiom 3 (condensed_detachment) }
% 92.81/12.36    fresh2(is_a_theorem(equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.36  = { by lemma 13 R->L }
% 92.81/12.36    fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.36  = { by axiom 2 (condensed_detachment) R->L }
% 92.81/12.36    fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.37  = { by axiom 1 (condensed_detachment) R->L }
% 92.81/12.37    fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.37  = { by axiom 1 (condensed_detachment) R->L }
% 92.81/12.37    fresh2(fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.37  = { by axiom 5 (p_1) R->L }
% 92.81/12.37    fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.37  = { by lemma 8 }
% 92.81/12.37    fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.37  = { by lemma 12 }
% 92.81/12.37    fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.37  = { by axiom 3 (condensed_detachment) }
% 92.81/12.37    fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.37  = { by axiom 2 (condensed_detachment) R->L }
% 92.81/12.37    fresh2(fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.37  = { by axiom 1 (condensed_detachment) R->L }
% 92.81/12.37    fresh2(fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.37  = { by axiom 1 (condensed_detachment) R->L }
% 92.81/12.37    fresh2(fresh2(fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.38  = { by lemma 10 R->L }
% 92.81/12.38    fresh2(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.38  = { by lemma 12 }
% 92.81/12.38    fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.38  = { by axiom 3 (condensed_detachment) R->L }
% 92.81/12.38    fresh2(fresh2(fresh2(fresh(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.38  = { by lemma 12 R->L }
% 92.81/12.38    fresh2(fresh2(fresh2(fresh(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.38  = { by lemma 11 }
% 92.81/12.39    fresh2(fresh2(fresh2(fresh(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 92.81/12.39  = { by axiom 1 (condensed_detachment) }
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% 92.81/12.39  = { by axiom 2 (condensed_detachment) }
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% 92.81/12.39  = { by axiom 3 (condensed_detachment) }
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% 92.81/12.39  = { by axiom 2 (condensed_detachment) R->L }
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% 92.81/12.39  = { by axiom 1 (condensed_detachment) R->L }
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% 92.81/12.40  = { by axiom 1 (condensed_detachment) R->L }
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% 93.60/12.40  = { by axiom 1 (condensed_detachment) R->L }
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% 93.60/12.41  = { by lemma 10 R->L }
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% 93.60/12.41  = { by axiom 3 (condensed_detachment) R->L }
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% 93.60/12.42  = { by lemma 12 R->L }
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% 93.60/12.42  = { by lemma 13 R->L }
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% 93.60/12.43  = { by axiom 5 (p_1) }
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% 93.60/12.43  = { by axiom 1 (condensed_detachment) }
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% 93.60/12.43  = { by axiom 1 (condensed_detachment) }
% 93.60/12.43    fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(c, c), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(c, c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), equivalent(equivalent(equivalent(c, c), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(c, c), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(c, c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))))), true, equivalent(equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(c, c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))))), true, equivalent(equivalent(equivalent(equivalent(c, c), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), true, equivalent(equivalent(equivalent(c, c), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 93.60/12.44  = { by axiom 2 (condensed_detachment) }
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% 93.60/12.44  = { by lemma 13 }
% 93.60/12.44    fresh2(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(c, c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))))), true, equivalent(equivalent(equivalent(equivalent(c, c), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), true, equivalent(equivalent(equivalent(c, c), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 93.60/12.44  = { by lemma 8 }
% 93.60/12.44    fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, c), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))))), true, equivalent(equivalent(equivalent(c, c), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 93.60/12.44  = { by axiom 3 (condensed_detachment) }
% 93.60/12.44    fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, c), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 93.60/12.44  = { by axiom 5 (p_1) }
% 93.60/12.44    fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 93.60/12.44  = { by axiom 1 (condensed_detachment) }
% 93.60/12.44    fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))))), true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 93.60/12.44  = { by axiom 1 (condensed_detachment) }
% 93.60/12.44    fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(c, b), e), equivalent(equivalent(c, b), equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e))))), true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 93.60/12.44  = { by axiom 1 (condensed_detachment) }
% 93.60/12.44    fresh2(fresh2(true, true, equivalent(e, equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(equivalent(c, b), e)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 93.60/12.44  = { by axiom 1 (condensed_detachment) }
% 93.60/12.44    fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, c)), equivalent(b, c)), e), e))
% 93.60/12.44  = { by axiom 1 (condensed_detachment) }
% 93.60/12.44    true
% 93.60/12.44  % SZS output end Proof
% 93.60/12.44  
% 93.60/12.44  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------