%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LCL096-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 08:17:24 EDT 2023

% Result   : Unsatisfiable 7.56s 1.32s
% Output   : Proof 7.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL096-10 : TPTP v8.1.2. Released v7.3.0.
% 0.13/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34  % Computer : n003.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 04:39:53 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 7.56/1.32  Command-line arguments: --no-flatten-goal
% 7.56/1.32  
% 7.56/1.32  % SZS status Unsatisfiable
% 7.56/1.32  
% 7.56/1.36  % SZS output start Proof
% 7.56/1.36  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 7.56/1.36  Axiom 2 (condensed_detachment): ifeq(is_a_theorem(equivalent(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 7.56/1.36  Axiom 3 (lg_2): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)) = true.
% 7.56/1.36  Axiom 4 (lg_4): is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), W), equivalent(equivalent(equivalent(X, V), Z), equivalent(equivalent(Y, V), W)))) = true.
% 7.56/1.36  Axiom 5 (lg_3): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V), V)) = true.
% 7.56/1.36  
% 7.56/1.36  Lemma 6: ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W)), true, is_a_theorem(W), true) = true.
% 7.56/1.36  Proof:
% 7.56/1.36    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W)), true, is_a_theorem(W), true)
% 7.56/1.36  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.36    ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W)), true, is_a_theorem(W), true), true)
% 7.56/1.36  = { by axiom 3 (lg_2) R->L }
% 7.56/1.36    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W)), true, is_a_theorem(W), true), true)
% 7.56/1.36  = { by axiom 2 (condensed_detachment) }
% 7.56/1.36    true
% 7.56/1.36  
% 7.56/1.36  Lemma 7: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z)))) = true.
% 7.56/1.36  Proof:
% 7.56/1.36    is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z))))
% 7.56/1.36  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.36    ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z)))), true)
% 7.56/1.36  = { by axiom 4 (lg_4) R->L }
% 7.56/1.36    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, W), equivalent(X, Z)), equivalent(W, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z))))), true, is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z)))), true)
% 7.56/1.36  = { by lemma 6 }
% 7.56/1.36    true
% 7.56/1.36  
% 7.56/1.36  Lemma 8: ifeq(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, is_a_theorem(equivalent(equivalent(W, Y), equivalent(W, Z))), true) = true.
% 7.56/1.36  Proof:
% 7.56/1.36    ifeq(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, is_a_theorem(equivalent(equivalent(W, Y), equivalent(W, Z))), true)
% 7.56/1.36  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.36    ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, is_a_theorem(equivalent(equivalent(W, Y), equivalent(W, Z))), true), true)
% 7.56/1.36  = { by lemma 7 R->L }
% 7.56/1.36    ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(W, Y), equivalent(W, Z)))), true, ifeq(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, is_a_theorem(equivalent(equivalent(W, Y), equivalent(W, Z))), true), true)
% 7.56/1.36  = { by axiom 2 (condensed_detachment) }
% 7.56/1.36    true
% 7.56/1.36  
% 7.56/1.36  Lemma 9: is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(Y, Z)))) = true.
% 7.56/1.36  Proof:
% 7.56/1.36    is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(Y, Z))))
% 7.56/1.36  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.36    ifeq(true, true, is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(Y, Z)))), true)
% 7.56/1.36  = { by lemma 7 R->L }
% 7.56/1.36    ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, W), equivalent(Y, Z)), equivalent(equivalent(Y, W), equivalent(Y, Z)))), true, is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(Y, Z)))), true)
% 7.56/1.37  = { by lemma 8 }
% 7.56/1.37    true
% 7.56/1.37  
% 7.56/1.37  Lemma 10: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))) = true.
% 7.56/1.37  Proof:
% 7.56/1.37    is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)))
% 7.56/1.37  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.37    ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))), true)
% 7.56/1.37  = { by lemma 9 R->L }
% 7.56/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))), true)
% 7.56/1.37  = { by lemma 6 }
% 7.56/1.37    true
% 7.56/1.37  
% 7.56/1.37  Lemma 11: ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(Y, Z))), W)), true, is_a_theorem(W), true) = true.
% 7.56/1.37  Proof:
% 7.56/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(Y, Z))), W)), true, is_a_theorem(W), true)
% 7.56/1.37  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(Y, Z))), W)), true, ifeq(true, true, is_a_theorem(W), true), true)
% 7.56/1.37  = { by lemma 9 R->L }
% 7.56/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(Y, Z))), W)), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(X, equivalent(Y, Z)))), true, is_a_theorem(W), true), true)
% 7.56/1.37  = { by axiom 2 (condensed_detachment) }
% 7.56/1.37    true
% 7.56/1.37  
% 7.56/1.37  Lemma 12: ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Y)), Z)), true, is_a_theorem(Z), true) = true.
% 7.56/1.37  Proof:
% 7.56/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Y)), Z)), true, is_a_theorem(Z), true)
% 7.56/1.37  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Y)), Z)), true, ifeq(true, true, is_a_theorem(Z), true), true)
% 7.56/1.37  = { by lemma 11 R->L }
% 7.56/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Y)), Z)), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(X, Y)), equivalent(W, equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(X, Y)))), true, is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Y))), true), true, is_a_theorem(Z), true), true)
% 7.56/1.37  = { by lemma 10 }
% 7.56/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Y)), Z)), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Y))), true), true, is_a_theorem(Z), true), true)
% 7.56/1.37  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Y)), Z)), true, ifeq(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Y))), true, is_a_theorem(Z), true), true)
% 7.56/1.37  = { by axiom 2 (condensed_detachment) }
% 7.56/1.37    true
% 7.56/1.37  
% 7.56/1.37  Lemma 13: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W))) = true.
% 7.56/1.37  Proof:
% 7.56/1.37    is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)))
% 7.56/1.37  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.37    ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W))), true)
% 7.56/1.37  = { by axiom 2 (condensed_detachment) R->L }
% 7.56/1.37    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(X, Y)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(X, Y)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(Z, Y), W))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W))), true)
% 7.56/1.37  = { by axiom 3 (lg_2) }
% 7.56/1.37    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(X, Y)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W))), true)
% 7.56/1.37  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.37    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(X, Y)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W))), true)
% 7.56/1.37  = { by axiom 4 (lg_4) }
% 7.56/1.37    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W))), true)
% 7.56/1.37  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W)))), true, is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), W)), equivalent(equivalent(Z, Y), W))), true)
% 7.56/1.37  = { by lemma 6 }
% 7.56/1.37    true
% 7.56/1.37  
% 7.56/1.37  Lemma 14: ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), true, is_a_theorem(equivalent(equivalent(Y, Z), W)), true) = true.
% 7.56/1.37  Proof:
% 7.56/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), true, is_a_theorem(equivalent(equivalent(Y, Z), W)), true)
% 7.56/1.37  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.37    ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), true, is_a_theorem(equivalent(equivalent(Y, Z), W)), true), true)
% 7.56/1.37  = { by lemma 11 R->L }
% 7.56/1.37    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), true, is_a_theorem(equivalent(equivalent(Y, Z), W)), true), true)
% 7.56/1.37  = { by axiom 5 (lg_3) }
% 7.56/1.37    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), true, is_a_theorem(equivalent(equivalent(Y, Z), W)), true), true)
% 7.56/1.37  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), true, is_a_theorem(equivalent(equivalent(Y, Z), W)), true), true)
% 7.56/1.37  = { by axiom 2 (condensed_detachment) }
% 7.56/1.37    true
% 7.56/1.37  
% 7.56/1.37  Goal 1 (prove_lg_1): is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)) = true.
% 7.56/1.37  Proof:
% 7.56/1.37    is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 7.56/1.37  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.37    ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.37  = { by axiom 2 (condensed_detachment) R->L }
% 7.56/1.37    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.38  = { by lemma 13 }
% 7.56/1.38    ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.38  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.38    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.38  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.38    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.38  = { by lemma 14 R->L }
% 7.56/1.38    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.38  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.38    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.38  = { by axiom 3 (lg_2) R->L }
% 7.56/1.38    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(b, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.38  = { by lemma 14 }
% 7.56/1.38    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.38  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.38    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.38  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.39    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.39  = { by axiom 2 (condensed_detachment) R->L }
% 7.56/1.39    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.39  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.39    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.40  = { by lemma 12 R->L }
% 7.56/1.40    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(X, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.40  = { by lemma 10 }
% 7.56/1.40    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.40  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.41    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.41  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.41    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.41  = { by lemma 8 R->L }
% 7.56/1.41    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, b), Z), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(Y, b), Z), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.41  = { by axiom 4 (lg_4) }
% 7.56/1.42    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.42  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.42    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.42  = { by axiom 2 (condensed_detachment) }
% 7.56/1.42    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.43  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.43    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.43  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.43    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.43  = { by lemma 12 R->L }
% 7.56/1.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.43  = { by axiom 4 (lg_4) }
% 7.56/1.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.44  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.44    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.44  = { by lemma 6 }
% 7.56/1.44    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.44  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.44    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.44  = { by axiom 2 (condensed_detachment) }
% 7.56/1.44    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.44  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.44    ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 7.56/1.44  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.44    ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 7.56/1.44  = { by lemma 8 R->L }
% 7.56/1.44    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 7.56/1.44  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.44    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 7.56/1.44  = { by lemma 13 R->L }
% 7.56/1.44    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 7.56/1.44  = { by axiom 1 (ifeq_axiom) R->L }
% 7.56/1.44    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 7.56/1.44  = { by lemma 8 R->L }
% 7.56/1.44    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), W), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), W), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 7.56/1.44  = { by lemma 13 }
% 7.56/1.45    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 7.56/1.45  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.45    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 7.56/1.45  = { by axiom 2 (condensed_detachment) }
% 7.56/1.45    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 7.56/1.45  = { by axiom 1 (ifeq_axiom) }
% 7.56/1.45    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 7.56/1.45  = { by axiom 2 (condensed_detachment) }
% 7.56/1.45    true
% 7.56/1.45  % SZS output end Proof
% 7.56/1.45  
% 7.56/1.45  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------