%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL089-1 : 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 : n011.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 08:17:22 EDT 2023

% Result   : Unsatisfiable 0.20s 0.65s
% Output   : Proof 3.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL089-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13  % 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 : n011.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 06:42:08 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.65  Command-line arguments: --no-flatten-goal
% 0.20/0.65  
% 0.20/0.65  % SZS status Unsatisfiable
% 0.20/0.65  
% 0.20/0.70  % SZS output start Proof
% 0.20/0.70  Take the following subset of the input axioms:
% 0.20/0.70    fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(implies(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 0.20/0.70    fof(ic_JLukasiewicz_4, axiom, ![P, Q, R, S, T]: is_a_theorem(implies(implies(implies(P, Q), implies(R, S)), implies(T, implies(implies(S, P), implies(R, P)))))).
% 0.20/0.70    fof(prove_ic_4, negated_conjecture, ~is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c))))).
% 0.20/0.70  
% 0.20/0.70  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.70  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.70  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.70    fresh(y, y, x1...xn) = u
% 0.20/0.70    C => fresh(s, t, x1...xn) = v
% 0.20/0.70  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.70  variables of u and v.
% 0.20/0.70  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.70  input problem has no model of domain size 1).
% 0.20/0.70  
% 0.20/0.70  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.70  
% 0.20/0.70  Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.20/0.70  Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.20/0.70  Axiom 3 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.20/0.70  Axiom 4 (ic_JLukasiewicz_4): is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X))))) = true.
% 0.20/0.70  
% 0.20/0.70  Lemma 5: fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, W))), true, implies(V, implies(implies(W, X), implies(Z, X)))) = is_a_theorem(implies(V, implies(implies(W, X), implies(Z, X)))).
% 0.20/0.70  Proof:
% 0.20/0.70    fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, W))), true, implies(V, implies(implies(W, X), implies(Z, X))))
% 0.20/0.70  = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.70    fresh(is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X))))), true, implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X))))
% 0.20/0.70  = { by axiom 4 (ic_JLukasiewicz_4) }
% 0.20/0.70    fresh(true, true, implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X))))
% 0.20/0.70  = { by axiom 2 (condensed_detachment) }
% 0.20/0.70    is_a_theorem(implies(V, implies(implies(W, X), implies(Z, X))))
% 0.20/0.70  
% 0.20/0.70  Lemma 6: is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W)))) = true.
% 0.20/0.70  Proof:
% 0.20/0.70    is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.70  = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.70    fresh(true, true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.70  = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.70    fresh(fresh2(true, true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.70  = { by axiom 4 (ic_JLukasiewicz_4) R->L }
% 0.20/0.70    fresh(fresh2(is_a_theorem(implies(implies(implies(Y, W), implies(Z, X)), implies(V, implies(implies(X, Y), implies(Z, Y))))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.70  = { by lemma 5 }
% 0.20/0.70    fresh(is_a_theorem(implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.70  = { by axiom 3 (condensed_detachment) }
% 0.20/0.70    fresh2(is_a_theorem(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U))))), true, implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.70  = { by axiom 4 (ic_JLukasiewicz_4) }
% 0.20/0.70    fresh2(true, true, implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.70  = { by axiom 1 (condensed_detachment) }
% 0.20/0.70    true
% 0.20/0.70  
% 0.20/0.70  Lemma 7: fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W))), true, implies(V, implies(Y, W))) = is_a_theorem(implies(V, implies(Y, W))).
% 0.20/0.70  Proof:
% 0.20/0.70    fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W))), true, implies(V, implies(Y, W)))
% 0.20/0.70  = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.70    fresh(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W)))), true, implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W)))
% 0.20/0.70  = { by lemma 6 }
% 0.20/0.70    fresh(true, true, implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W)))
% 0.20/0.70  = { by axiom 2 (condensed_detachment) }
% 0.20/0.70    is_a_theorem(implies(V, implies(Y, W)))
% 0.20/0.70  
% 0.20/0.70  Lemma 8: is_a_theorem(implies(X, implies(Y, implies(Z, Y)))) = true.
% 0.20/0.70  Proof:
% 0.20/0.70    is_a_theorem(implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.70  = { by lemma 7 R->L }
% 0.20/0.70    fresh2(is_a_theorem(implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.70  = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.70    fresh2(fresh(true, true, implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.70  = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.70    fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y))))), true, implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.70  = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.70    fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(Z, Y), Y), implies(Y, implies(implies(Z, Y), Y)))), true, implies(implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y))))), true, implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.70  = { by axiom 4 (ic_JLukasiewicz_4) R->L }
% 0.20/0.70    fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2))))), true, implies(implies(implies(Z, Y), Y), implies(Y, implies(implies(Z, Y), Y)))), true, implies(implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y))))), true, implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.70  = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.70    fresh2(fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2)))), implies(implies(implies(Z, Y), Y), implies(Y, implies(implies(Z, Y), Y))))), true, implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2)))), implies(implies(implies(Z, Y), Y), implies(Y, implies(implies(Z, Y), Y)))), true, implies(implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y))))), true, implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.70  = { by lemma 7 R->L }
% 0.20/0.70    fresh2(fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(U2, Y), implies(implies(Z, Y), Y)), implies(Y, implies(implies(Z, Y), Y))), implies(implies(implies(Z, Y), Y), implies(Y, implies(implies(Z, Y), Y))))), true, implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2)))), implies(implies(implies(Z, Y), Y), implies(Y, implies(implies(Z, Y), Y))))), true, implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2)))), implies(implies(implies(Z, Y), Y), implies(Y, implies(implies(Z, Y), Y)))), true, implies(implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y))))), true, implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.70  = { by lemma 6 }
% 0.20/0.70    fresh2(fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2)))), implies(implies(implies(Z, Y), Y), implies(Y, implies(implies(Z, Y), Y))))), true, implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2)))), implies(implies(implies(Z, Y), Y), implies(Y, implies(implies(Z, Y), Y)))), true, implies(implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y))))), true, implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.71  = { by axiom 1 (condensed_detachment) }
% 0.20/0.71    fresh2(fresh(fresh2(fresh(true, true, implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(V2, implies(implies(W2, X2), implies(Z2, X2)))), implies(implies(implies(Z, Y), Y), implies(Y, implies(implies(Z, Y), Y)))), true, implies(implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y))))), true, implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.71  = { by axiom 2 (condensed_detachment) }
% 0.20/0.71    fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(Z, Y), Y), implies(Y, implies(implies(Z, Y), Y)))), true, implies(implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y))))), true, implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.71  = { by lemma 5 }
% 0.20/0.71    fresh2(fresh(is_a_theorem(implies(implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y))))), true, implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W)))), implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.71  = { by axiom 3 (condensed_detachment) }
% 0.20/0.71    fresh2(fresh2(is_a_theorem(implies(implies(implies(W, V), implies(U, T)), implies(S, implies(implies(T, W), implies(U, W))))), true, implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.71  = { by axiom 4 (ic_JLukasiewicz_4) }
% 0.20/0.71    fresh2(fresh2(true, true, implies(implies(implies(implies(Z, Y), Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.71  = { by axiom 1 (condensed_detachment) }
% 0.20/0.71    fresh2(true, true, implies(X, implies(Y, implies(Z, Y))))
% 0.20/0.71  = { by axiom 1 (condensed_detachment) }
% 0.20/0.71    true
% 0.20/0.71  
% 0.20/0.71  Lemma 9: is_a_theorem(implies(X, implies(Y, X))) = true.
% 0.20/0.71  Proof:
% 0.20/0.71    is_a_theorem(implies(X, implies(Y, X)))
% 0.20/0.71  = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.71    fresh(true, true, implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(X, implies(Y, X)))
% 0.20/0.71  = { by lemma 8 R->L }
% 0.20/0.71    fresh(is_a_theorem(implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(X, implies(Y, X)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(X, implies(Y, X)))
% 0.20/0.71  = { by axiom 3 (condensed_detachment) }
% 0.20/0.71    fresh2(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, implies(X, implies(Y, X)))
% 0.20/0.71  = { by axiom 4 (ic_JLukasiewicz_4) }
% 0.20/0.71    fresh2(true, true, implies(X, implies(Y, X)))
% 0.20/0.71  = { by axiom 1 (condensed_detachment) }
% 0.20/0.71    true
% 0.20/0.71  
% 0.20/0.71  Lemma 10: is_a_theorem(implies(X, implies(Y, implies(implies(Y, Z), implies(W, Z))))) = true.
% 0.20/0.71  Proof:
% 0.20/0.71    is_a_theorem(implies(X, implies(Y, implies(implies(Y, Z), implies(W, Z)))))
% 0.20/0.71  = { by lemma 7 R->L }
% 0.20/0.71    fresh2(is_a_theorem(implies(implies(implies(Z, Y), implies(W, Y)), implies(Y, implies(implies(Y, Z), implies(W, Z))))), true, implies(X, implies(Y, implies(implies(Y, Z), implies(W, Z)))))
% 0.20/0.71  = { by axiom 4 (ic_JLukasiewicz_4) }
% 0.20/0.71    fresh2(true, true, implies(X, implies(Y, implies(implies(Y, Z), implies(W, Z)))))
% 0.20/0.71  = { by axiom 1 (condensed_detachment) }
% 0.20/0.71    true
% 0.20/0.71  
% 0.20/0.71  Lemma 11: is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z))) = true.
% 0.20/0.71  Proof:
% 0.20/0.71    is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))
% 0.20/0.71  = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.71    fresh(true, true, implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))
% 0.20/0.71  = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.71    fresh(fresh2(true, true, implies(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))), true, implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))
% 0.20/0.71  = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.71    fresh(fresh2(fresh2(true, true, implies(implies(Z, W), implies(implies(implies(Z, W), Y), implies(X, Y)))), true, implies(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))), true, implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))
% 0.20/0.71  = { by axiom 4 (ic_JLukasiewicz_4) R->L }
% 0.20/0.71    fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, implies(implies(Z, W), implies(implies(implies(Z, W), Y), implies(X, Y)))), true, implies(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))), true, implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))
% 0.20/0.71  = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.71    fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(Z, W), implies(implies(implies(Z, W), Y), implies(X, Y))))), true, implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(Z, W), implies(implies(implies(Z, W), Y), implies(X, Y)))), true, implies(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))), true, implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))
% 0.20/0.71  = { by lemma 10 }
% 0.20/0.71    fresh(fresh2(fresh(true, true, implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(Z, W), implies(implies(implies(Z, W), Y), implies(X, Y)))), true, implies(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))), true, implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))
% 0.20/0.71  = { by axiom 2 (condensed_detachment) }
% 0.20/0.71    fresh(fresh2(is_a_theorem(implies(implies(Z, W), implies(implies(implies(Z, W), Y), implies(X, Y)))), true, implies(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))), true, implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))
% 0.20/0.71  = { by lemma 5 }
% 0.20/0.71    fresh(is_a_theorem(implies(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))), true, implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V)))), implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))
% 0.20/0.71  = { by axiom 3 (condensed_detachment) }
% 0.20/0.71    fresh2(is_a_theorem(implies(implies(implies(V, U), implies(T, S)), implies(X2, implies(implies(S, V), implies(T, V))))), true, implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))
% 0.20/0.71  = { by axiom 4 (ic_JLukasiewicz_4) }
% 0.20/0.71    fresh2(true, true, implies(implies(implies(X, Y), Z), implies(implies(implies(Z, W), Y), Z)))
% 0.20/0.71  = { by axiom 1 (condensed_detachment) }
% 0.20/0.71    true
% 0.20/0.71  
% 0.20/0.71  Goal 1 (prove_ic_4): is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))) = true.
% 0.20/0.71  Proof:
% 0.20/0.71    is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.71  = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.71    fresh(true, true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.71  = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.71    fresh(fresh2(true, true, implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.71  = { by axiom 4 (ic_JLukasiewicz_4) R->L }
% 0.20/0.71    fresh(fresh2(is_a_theorem(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.71  = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.72    fresh(fresh(is_a_theorem(implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.72  = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.72    fresh(fresh(fresh(true, true, implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.72  = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.72    fresh(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.72  = { by axiom 4 (ic_JLukasiewicz_4) R->L }
% 0.20/0.72    fresh(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, implies(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.73  = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.73    fresh(fresh(fresh(fresh(is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.73  = { by lemma 5 R->L }
% 0.20/0.73    fresh(fresh(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.73  = { by lemma 9 }
% 0.20/0.73    fresh(fresh(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.73  = { by axiom 1 (condensed_detachment) }
% 0.20/0.74    fresh(fresh(fresh(fresh(true, true, implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.74  = { by axiom 2 (condensed_detachment) }
% 0.20/0.74    fresh(fresh(fresh(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.74  = { by axiom 3 (condensed_detachment) }
% 0.20/0.74    fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.74  = { by lemma 11 }
% 0.20/0.74    fresh(fresh(fresh2(true, true, implies(implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.74  = { by axiom 1 (condensed_detachment) }
% 0.20/0.74    fresh(fresh(true, true, implies(implies(implies(Y, Z), implies(W, V)), implies(U, implies(implies(V, Y), implies(W, Y)))), implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.74  = { by axiom 2 (condensed_detachment) }
% 0.20/0.74    fresh(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.74  = { by axiom 3 (condensed_detachment) }
% 0.20/0.74    fresh2(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.74  = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.74    fresh2(fresh(true, true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.74  = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.74    fresh2(fresh(fresh2(true, true, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.74  = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.74    fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.74  = { by axiom 4 (ic_JLukasiewicz_4) R->L }
% 0.20/0.74    fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 0.20/0.74  = { by axiom 3 (condensed_detachment) R->L }
% 2.85/0.74    fresh2(fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.74  = { by lemma 5 R->L }
% 2.85/0.74    fresh2(fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), X3), implies(implies(a, b), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.75  = { by lemma 10 }
% 2.85/0.75    fresh2(fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.75  = { by axiom 1 (condensed_detachment) }
% 2.85/0.75    fresh2(fresh(fresh2(fresh(true, true, implies(implies(implies(W2, V2), implies(U2, T2)), implies(S2, implies(implies(T2, W2), implies(U2, W2)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.75  = { by axiom 2 (condensed_detachment) }
% 2.85/0.75    fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.75  = { by axiom 3 (condensed_detachment) R->L }
% 2.85/0.75    fresh2(fresh(fresh(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.75  = { by axiom 2 (condensed_detachment) R->L }
% 2.85/0.75    fresh2(fresh(fresh(fresh(true, true, implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.75  = { by lemma 11 R->L }
% 2.85/0.75    fresh2(fresh(fresh(fresh(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.75  = { by axiom 3 (condensed_detachment) }
% 2.85/0.75    fresh2(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.75  = { by lemma 9 }
% 2.85/0.75    fresh2(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.75  = { by axiom 1 (condensed_detachment) }
% 2.85/0.75    fresh2(fresh(fresh(true, true, implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.76  = { by axiom 2 (condensed_detachment) }
% 2.85/0.76    fresh2(fresh(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.76  = { by axiom 3 (condensed_detachment) }
% 2.85/0.76    fresh2(fresh2(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.76  = { by axiom 2 (condensed_detachment) R->L }
% 2.85/0.76    fresh2(fresh2(fresh(true, true, implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.76  = { by axiom 1 (condensed_detachment) R->L }
% 2.85/0.76    fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.76  = { by axiom 4 (ic_JLukasiewicz_4) R->L }
% 2.85/0.76    fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(T3, implies(implies(U3, Z3), implies(V3, Z3))))), true, implies(implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.76  = { by axiom 3 (condensed_detachment) R->L }
% 2.85/0.76    fresh2(fresh2(fresh(fresh(is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(T3, implies(implies(U3, Z3), implies(V3, Z3)))), implies(implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(Z3, W3), implies(V3, U3)), implies(T3, implies(implies(U3, Z3), implies(V3, Z3)))), implies(implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.85/0.76  = { by lemma 5 R->L }
% 3.15/0.76    fresh2(fresh2(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), S3), implies(implies(a, b), implies(implies(c, Y3), implies(a, b))))), true, implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(T3, implies(implies(U3, Z3), implies(V3, Z3)))), implies(implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(Z3, W3), implies(V3, U3)), implies(T3, implies(implies(U3, Z3), implies(V3, Z3)))), implies(implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 3.15/0.76  = { by lemma 8 }
% 3.15/0.76    fresh2(fresh2(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(T3, implies(implies(U3, Z3), implies(V3, Z3)))), implies(implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(Z3, W3), implies(V3, U3)), implies(T3, implies(implies(U3, Z3), implies(V3, Z3)))), implies(implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 3.15/0.76  = { by axiom 1 (condensed_detachment) }
% 3.15/0.76    fresh2(fresh2(fresh(fresh(true, true, implies(implies(implies(Z3, W3), implies(V3, U3)), implies(T3, implies(implies(U3, Z3), implies(V3, Z3)))), implies(implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 3.15/0.76  = { by axiom 2 (condensed_detachment) }
% 3.15/0.76    fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 3.15/0.76  = { by axiom 3 (condensed_detachment) }
% 3.15/0.76    fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(c, Y3), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 3.15/0.76  = { by axiom 4 (ic_JLukasiewicz_4) }
% 3.15/0.76    fresh2(fresh2(fresh2(true, true, implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 3.15/0.76  = { by axiom 1 (condensed_detachment) }
% 3.15/0.76    fresh2(fresh2(true, true, implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), X), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 3.15/0.76  = { by axiom 1 (condensed_detachment) }
% 3.15/0.76    fresh2(true, true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 3.15/0.76  = { by axiom 1 (condensed_detachment) }
% 3.15/0.76    true
% 3.15/0.76  % SZS output end Proof
% 3.15/0.76  
% 3.15/0.76  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------