%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL024-10 : TPTP v8.1.2. Released v7.5.0.
% 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 : n013.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 08:17:04 EDT 2023

% Result   : Unsatisfiable 59.46s 8.23s
% Output   : Proof 60.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL024-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri Aug 25 06:04:17 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 59.46/8.23  Command-line arguments: --no-flatten-goal
% 59.46/8.23  
% 59.46/8.23  % SZS status Unsatisfiable
% 59.46/8.23  
% 59.46/8.27  % SZS output start Proof
% 59.46/8.27  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 59.46/8.27  Axiom 2 (xgk): is_a_theorem(equivalent(X, equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y)))) = true.
% 59.46/8.27  Axiom 3 (condensed_detachment): ifeq(is_a_theorem(equivalent(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 59.46/8.27  
% 59.46/8.27  Lemma 4: ifeq(is_a_theorem(X), true, is_a_theorem(equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y))), true) = true.
% 59.46/8.27  Proof:
% 59.46/8.27    ifeq(is_a_theorem(X), true, is_a_theorem(equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y))), true)
% 59.46/8.27  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.27    ifeq(true, true, ifeq(is_a_theorem(X), true, is_a_theorem(equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y))), true), true)
% 59.46/8.27  = { by axiom 2 (xgk) R->L }
% 59.46/8.27    ifeq(is_a_theorem(equivalent(X, equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y)))), true, ifeq(is_a_theorem(X), true, is_a_theorem(equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y))), true), true)
% 59.46/8.27  = { by axiom 3 (condensed_detachment) }
% 59.46/8.27    true
% 59.46/8.27  
% 59.46/8.27  Lemma 5: is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))), equivalent(Y, X))) = true.
% 59.46/8.27  Proof:
% 59.46/8.27    is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))), equivalent(Y, X)))
% 59.46/8.27  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.27    ifeq(true, true, is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))), equivalent(Y, X))), true)
% 59.46/8.27  = { by axiom 2 (xgk) R->L }
% 59.46/8.27    ifeq(is_a_theorem(equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), true, is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))), equivalent(Y, X))), true)
% 59.46/8.27  = { by lemma 4 }
% 59.46/8.27    true
% 59.46/8.27  
% 59.46/8.27  Lemma 6: ifeq(is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))))), true, is_a_theorem(equivalent(Y, X)), true) = true.
% 59.46/8.27  Proof:
% 59.46/8.27    ifeq(is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))))), true, is_a_theorem(equivalent(Y, X)), true)
% 59.46/8.27  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.27    ifeq(true, true, ifeq(is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))))), true, is_a_theorem(equivalent(Y, X)), true), true)
% 59.46/8.27  = { by lemma 5 R->L }
% 59.46/8.27    ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))), equivalent(Y, X))), true, ifeq(is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))))), true, is_a_theorem(equivalent(Y, X)), true), true)
% 59.46/8.27  = { by axiom 3 (condensed_detachment) }
% 59.46/8.27    true
% 59.46/8.27  
% 59.46/8.27  Lemma 7: ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y))), W)), true, is_a_theorem(W), true) = true.
% 59.46/8.27  Proof:
% 59.46/8.27    ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y))), W)), true, is_a_theorem(W), true)
% 59.46/8.27  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.27    ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y))), W)), true, ifeq(true, true, is_a_theorem(W), true), true)
% 59.46/8.27  = { by axiom 2 (xgk) R->L }
% 59.46/8.28    ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y))), W)), true, ifeq(is_a_theorem(equivalent(X, equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y)))), true, is_a_theorem(W), true), true)
% 59.46/8.28  = { by axiom 3 (condensed_detachment) }
% 59.46/8.28    true
% 59.46/8.28  
% 59.46/8.28  Lemma 8: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), W)) = true.
% 59.46/8.28  Proof:
% 59.46/8.28    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), W))
% 59.46/8.28  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.28    ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), W)), true)
% 59.46/8.28  = { by lemma 5 R->L }
% 59.46/8.28    ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), equivalent(Z, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X))))), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), W))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), W)), true)
% 59.46/8.28  = { by lemma 7 }
% 59.46/8.28    true
% 59.46/8.28  
% 59.46/8.28  Lemma 9: is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y)) = true.
% 59.46/8.28  Proof:
% 59.46/8.28    is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y))
% 59.46/8.28  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.28    ifeq(true, true, is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y)), true)
% 59.46/8.28  = { by lemma 4 R->L }
% 59.46/8.28    ifeq(ifeq(is_a_theorem(equivalent(X, X)), true, is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, X))), equivalent(equivalent(X, equivalent(X, Y)), Y))), true), true, is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y)), true)
% 59.46/8.28  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.28    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(X, X)), true), true, is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, X))), equivalent(equivalent(X, equivalent(X, Y)), Y))), true), true, is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y)), true)
% 59.46/8.28  = { by lemma 8 R->L }
% 59.46/8.28    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z, equivalent(X, X)), equivalent(X, Z)), equivalent(X, equivalent(Z, equivalent(X, X)))), equivalent(Z, equivalent(X, X)))), true, is_a_theorem(equivalent(X, X)), true), true, is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, X))), equivalent(equivalent(X, equivalent(X, Y)), Y))), true), true, is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y)), true)
% 59.46/8.28  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.28    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z, equivalent(X, X)), equivalent(X, Z)), equivalent(X, equivalent(Z, equivalent(X, X)))), equivalent(Z, equivalent(X, X)))), true, is_a_theorem(equivalent(X, X)), true), true), true, is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, X))), equivalent(equivalent(X, equivalent(X, Y)), Y))), true), true, is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y)), true)
% 59.46/8.28  = { by lemma 8 R->L }
% 59.46/8.28    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z, equivalent(X, X)), equivalent(X, Z)), equivalent(X, equivalent(Z, equivalent(X, X)))), equivalent(Z, equivalent(X, X))), equivalent(X, X))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z, equivalent(X, X)), equivalent(X, Z)), equivalent(X, equivalent(Z, equivalent(X, X)))), equivalent(Z, equivalent(X, X)))), true, is_a_theorem(equivalent(X, X)), true), true), true, is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, X))), equivalent(equivalent(X, equivalent(X, Y)), Y))), true), true, is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y)), true)
% 59.46/8.28  = { by axiom 3 (condensed_detachment) }
% 59.46/8.28    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, X))), equivalent(equivalent(X, equivalent(X, Y)), Y))), true), true, is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y)), true)
% 59.46/8.28  = { by axiom 1 (ifeq_axiom) }
% 59.46/8.28    ifeq(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, X))), equivalent(equivalent(X, equivalent(X, Y)), Y))), true, is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y)), true)
% 59.46/8.28  = { by lemma 7 }
% 59.46/8.28    true
% 59.46/8.28  
% 59.46/8.28  Lemma 10: is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))) = true.
% 59.46/8.28  Proof:
% 59.46/8.28    is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))
% 59.46/8.28  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.28    ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), true)
% 59.46/8.28  = { by lemma 6 R->L }
% 59.46/8.28    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), equivalent(Z, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), true)
% 59.46/8.28  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.28    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), equivalent(Z, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), true)
% 59.46/8.28  = { by lemma 9 R->L }
% 59.46/8.28    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), equivalent(Z, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)))))), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), equivalent(Z, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), equivalent(Z, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), true)
% 59.46/8.28  = { by lemma 6 }
% 59.46/8.28    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), true)
% 59.46/8.28  = { by axiom 1 (ifeq_axiom) }
% 59.46/8.28    ifeq(is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))))), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), true)
% 59.46/8.28  = { by lemma 6 }
% 59.46/8.28    true
% 59.46/8.28  
% 59.46/8.28  Lemma 11: is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, Y)))) = true.
% 59.46/8.28  Proof:
% 59.46/8.28    is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, Y))))
% 59.46/8.28  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.28    ifeq(true, true, is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, Y)))), true)
% 59.46/8.28  = { by lemma 10 R->L }
% 59.46/8.28    ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, Y)))))), true, is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, Y)))), true)
% 59.46/8.28  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.28    ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, Y)))))), true, is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, Y)))), true), true)
% 59.46/8.28  = { by lemma 9 R->L }
% 59.46/8.28    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, Y))))), equivalent(X, equivalent(Y, equivalent(X, Y))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, Y)))))), true, is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, Y)))), true), true)
% 59.46/8.28  = { by axiom 3 (condensed_detachment) }
% 59.46/8.29    true
% 59.46/8.29  
% 59.46/8.29  Lemma 12: is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(W, equivalent(Z, W))))), equivalent(Y, X))) = true.
% 59.46/8.29  Proof:
% 59.46/8.29    is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(W, equivalent(Z, W))))), equivalent(Y, X)))
% 59.46/8.29  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.29    ifeq(true, true, is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(W, equivalent(Z, W))))), equivalent(Y, X))), true)
% 59.46/8.29  = { by lemma 11 R->L }
% 59.46/8.29    ifeq(is_a_theorem(equivalent(Z, equivalent(W, equivalent(Z, W)))), true, is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(W, equivalent(Z, W))))), equivalent(Y, X))), true)
% 59.46/8.29  = { by lemma 4 }
% 59.46/8.29    true
% 59.46/8.29  
% 59.46/8.29  Lemma 13: ifeq(is_a_theorem(equivalent(X, equivalent(Y, X))), true, is_a_theorem(Y), true) = true.
% 59.46/8.29  Proof:
% 59.46/8.29    ifeq(is_a_theorem(equivalent(X, equivalent(Y, X))), true, is_a_theorem(Y), true)
% 59.46/8.29  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.29    ifeq(true, true, ifeq(is_a_theorem(equivalent(X, equivalent(Y, X))), true, is_a_theorem(Y), true), true)
% 59.46/8.29  = { by axiom 3 (condensed_detachment) R->L }
% 59.46/8.29    ifeq(ifeq(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(X, equivalent(Y, X))))), equivalent(equivalent(X, equivalent(Y, X)), Y))), true, ifeq(is_a_theorem(equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(X, equivalent(Y, X)))))), true, is_a_theorem(equivalent(equivalent(X, equivalent(Y, X)), Y)), true), true), true, ifeq(is_a_theorem(equivalent(X, equivalent(Y, X))), true, is_a_theorem(Y), true), true)
% 59.46/8.29  = { by lemma 11 }
% 59.46/8.29    ifeq(ifeq(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(X, equivalent(Y, X))))), equivalent(equivalent(X, equivalent(Y, X)), Y))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(X, equivalent(Y, X)), Y)), true), true), true, ifeq(is_a_theorem(equivalent(X, equivalent(Y, X))), true, is_a_theorem(Y), true), true)
% 59.46/8.29  = { by axiom 1 (ifeq_axiom) }
% 59.46/8.29    ifeq(ifeq(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(X, equivalent(Y, X))))), equivalent(equivalent(X, equivalent(Y, X)), Y))), true, is_a_theorem(equivalent(equivalent(X, equivalent(Y, X)), Y)), true), true, ifeq(is_a_theorem(equivalent(X, equivalent(Y, X))), true, is_a_theorem(Y), true), true)
% 59.46/8.29  = { by lemma 12 }
% 59.46/8.29    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(X, equivalent(Y, X)), Y)), true), true, ifeq(is_a_theorem(equivalent(X, equivalent(Y, X))), true, is_a_theorem(Y), true), true)
% 59.46/8.29  = { by axiom 1 (ifeq_axiom) }
% 59.46/8.29    ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(Y, X)), Y)), true, ifeq(is_a_theorem(equivalent(X, equivalent(Y, X))), true, is_a_theorem(Y), true), true)
% 59.46/8.29  = { by axiom 3 (condensed_detachment) }
% 59.46/8.29    true
% 59.46/8.29  
% 59.46/8.29  Goal 1 (prove_pyo): is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))) = true.
% 59.46/8.29  Proof:
% 59.46/8.29    is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 59.46/8.29  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.29    ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true)
% 59.46/8.29  = { by lemma 13 R->L }
% 59.46/8.29    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(b, a)), equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(b, a))))), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true)
% 59.46/8.29  = { by lemma 10 }
% 59.46/8.29    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true)
% 59.46/8.29  = { by axiom 1 (ifeq_axiom) }
% 59.46/8.29    ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true)
% 59.46/8.29  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.29    ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true), true)
% 59.46/8.29  = { by lemma 13 R->L }
% 59.46/8.29    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true), true)
% 59.46/8.30  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.30    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true), true)
% 59.46/8.31  = { by lemma 6 R->L }
% 59.46/8.31    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true), true)
% 59.46/8.33  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.33    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true), true)
% 59.46/8.34  = { by lemma 12 R->L }
% 59.46/8.34    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true), true)
% 59.46/8.35  = { by axiom 1 (ifeq_axiom) R->L }
% 59.46/8.36    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), 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% 59.46/8.36  = { by lemma 9 R->L }
% 60.18/8.37    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true), true)
% 60.18/8.37  = { by axiom 3 (condensed_detachment) }
% 60.18/8.37    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true), true)
% 60.18/8.37  = { by axiom 1 (ifeq_axiom) }
% 60.18/8.37    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true), true)
% 60.18/8.37  = { by lemma 6 }
% 60.18/8.37    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true), true)
% 60.18/8.37  = { by axiom 1 (ifeq_axiom) }
% 60.18/8.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), true), true)
% 60.18/8.37  = { by axiom 3 (condensed_detachment) }
% 60.18/8.37    true
% 60.18/8.37  % SZS output end Proof
% 60.18/8.37  
% 60.18/8.37  RESULT: Unsatisfiable (the axioms are contradictory).
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