Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL123-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:49:06 AM UTC 2026

% Result   : Unsatisfiable 28.45s 4.08s
% Output   : Proof 170.92s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL123-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38  % Computer : n017.cluster.edu
% 0.12/0.38  % Model    : x86_64 x86_64
% 0.12/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38  % Memory   : 8046.5625MB
% 0.12/0.38  % OS       : Linux 6.8.0-71-generic
% 0.12/0.38  % CPULimit : 300
% 0.12/0.38  % WCLimit  : 300
% 0.12/0.38  % DateTime : Sun Sep 27 15:18:04 UTC 2026
% 0.12/0.38  % CPUTime  : 
% 0.12/0.38  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.45/4.08  Command-line arguments: --no-flatten-goal
% 28.45/4.08  
% 28.45/4.08  % SZS status Unsatisfiable
% 28.45/4.08  
% 102.88/15.22  % SZS output start Proof
% 102.88/15.22  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 102.88/15.22  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.
% 103.59/15.36  Axiom 3 (lg_2): is_a_theorem(equivalent(X, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W)))))) = true.
% 103.59/15.36  
% 103.59/15.36  Goal 1 (prove_lg_4): is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))) = true.
% 103.59/15.36  Proof:
% 103.59/15.36    is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))
% 103.59/15.36  = { by axiom 1 (ifeq_axiom) R->L }
% 103.59/15.37    ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 103.59/15.37  = { by axiom 2 (condensed_detachment) R->L }
% 103.59/15.37    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 103.59/15.37  = { by axiom 1 (ifeq_axiom) R->L }
% 103.59/15.37    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 103.59/15.37  = { by axiom 2 (condensed_detachment) R->L }
% 103.59/15.38    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 103.59/15.38  = { by axiom 3 (lg_2) }
% 103.59/15.38    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 103.59/15.38  = { by axiom 1 (ifeq_axiom) }
% 103.59/15.39    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 103.59/15.39  = { by axiom 3 (lg_2) }
% 103.59/15.39    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 103.59/15.40  = { by axiom 1 (ifeq_axiom) }
% 104.28/15.40    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 104.28/15.41  = { by axiom 1 (ifeq_axiom) R->L }
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% 104.28/15.42  = { by axiom 2 (condensed_detachment) R->L }
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% 104.28/15.44  = { by axiom 1 (ifeq_axiom) R->L }
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% 104.28/15.46  = { by axiom 2 (condensed_detachment) R->L }
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% 107.82/16.04  = { by axiom 2 (condensed_detachment) }
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% 107.82/16.06  = { by axiom 1 (ifeq_axiom) }
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% 108.92/16.08  = { by axiom 1 (ifeq_axiom) R->L }
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% 115.75/17.08  = { by axiom 2 (condensed_detachment) }
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% 115.75/17.10  = { by axiom 1 (ifeq_axiom) }
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% 116.47/17.13  = { by axiom 1 (ifeq_axiom) R->L }
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% 119.04/17.57  = { by axiom 2 (condensed_detachment) R->L }
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% 142.83/20.92  = { by axiom 2 (condensed_detachment) }
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% 142.83/20.94  = { by axiom 1 (ifeq_axiom) }
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% 142.83/20.97  = { by axiom 1 (ifeq_axiom) R->L }
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% 167.37/24.47  = { by axiom 2 (condensed_detachment) }
% 167.37/24.48    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(a, equivalent(e, equivalent(c, f))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), 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% 167.37/24.48  = { by axiom 1 (ifeq_axiom) }
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% 167.37/24.48  = { by axiom 2 (condensed_detachment) }
% 167.37/24.48    ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 167.37/24.48  = { by axiom 1 (ifeq_axiom) }
% 167.37/24.49    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 167.37/24.49  = { by axiom 1 (ifeq_axiom) R->L }
% 167.37/24.49    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 167.37/24.49  = { by axiom 2 (condensed_detachment) R->L }
% 167.37/24.49    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 167.37/24.49  = { by axiom 1 (ifeq_axiom) R->L }
% 167.37/24.49    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 167.37/24.49  = { by axiom 3 (lg_2) R->L }
% 167.37/24.50    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, ifeq(ifeq(is_a_theorem(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9)))))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 167.37/24.50  = { by axiom 1 (ifeq_axiom) R->L }
% 168.08/24.50    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9)))))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.50  = { by axiom 2 (condensed_detachment) R->L }
% 168.08/24.50    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9))))), equivalent(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9))))), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(is_a_theorem(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9)))))), true, is_a_theorem(equivalent(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9))))), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9)))))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.50  = { by axiom 3 (lg_2) }
% 168.08/24.51    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9)))))), true, is_a_theorem(equivalent(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9))))), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9)))))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.51  = { by axiom 1 (ifeq_axiom) }
% 168.08/24.51    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9)))))), true, is_a_theorem(equivalent(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9))))), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9)))))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.51  = { by axiom 3 (lg_2) }
% 168.08/24.51    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9))))), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9)))))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.51  = { by axiom 1 (ifeq_axiom) }
% 168.08/24.52    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9))))), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, ifeq(is_a_theorem(equivalent(W9, equivalent(W9, equivalent(equivalent(V9, U9), equivalent(equivalent(V9, T9), equivalent(U9, T9)))))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.52  = { by axiom 2 (condensed_detachment) }
% 168.08/24.52    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.52  = { by axiom 1 (ifeq_axiom) }
% 168.08/24.52    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.52  = { by axiom 1 (ifeq_axiom) R->L }
% 168.08/24.52    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.52  = { by axiom 2 (condensed_detachment) R->L }
% 168.08/24.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))))), true, ifeq(is_a_theorem(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.53  = { by axiom 1 (ifeq_axiom) R->L }
% 168.08/24.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))))), true), true, ifeq(is_a_theorem(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.53  = { by axiom 3 (lg_2) R->L }
% 168.08/24.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10)))))), true, is_a_theorem(equivalent(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))))), true), true, ifeq(is_a_theorem(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.54  = { by axiom 1 (ifeq_axiom) R->L }
% 168.08/24.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10)))))), true, is_a_theorem(equivalent(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))))), true), true), true, ifeq(is_a_theorem(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.54  = { by axiom 3 (lg_2) R->L }
% 168.08/24.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10))))), equivalent(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))))), true, ifeq(is_a_theorem(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10)))))), true, is_a_theorem(equivalent(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))))), true), true), true, ifeq(is_a_theorem(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.55  = { by axiom 2 (condensed_detachment) }
% 168.08/24.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.56  = { by axiom 1 (ifeq_axiom) }
% 168.08/24.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(S9, equivalent(S9, equivalent(equivalent(X10, Y10), equivalent(equivalent(X10, Z10), equivalent(Y10, Z10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.56  = { by axiom 3 (lg_2) }
% 168.08/24.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.56  = { by axiom 1 (ifeq_axiom) }
% 168.08/24.56    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.56  = { by axiom 1 (ifeq_axiom) R->L }
% 168.08/24.56    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.56  = { by axiom 3 (lg_2) R->L }
% 168.08/24.57    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.57  = { by axiom 2 (condensed_detachment) }
% 168.08/24.57    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.57  = { by axiom 1 (ifeq_axiom) }
% 168.08/24.57    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.57  = { by axiom 1 (ifeq_axiom) R->L }
% 168.08/24.57    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.58  = { by axiom 2 (condensed_detachment) R->L }
% 168.08/24.58    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.58  = { by axiom 1 (ifeq_axiom) R->L }
% 168.08/24.58    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.59  = { by axiom 3 (lg_2) R->L }
% 168.08/24.59    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(ifeq(is_a_theorem(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.59  = { by axiom 1 (ifeq_axiom) R->L }
% 168.08/24.59    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.60  = { by axiom 2 (condensed_detachment) R->L }
% 168.08/24.60    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10))))), equivalent(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))))), true, ifeq(is_a_theorem(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10)))))), true, is_a_theorem(equivalent(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, ifeq(is_a_theorem(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.08/24.60  = { by axiom 3 (lg_2) }
% 168.80/24.61    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10)))))), true, is_a_theorem(equivalent(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, ifeq(is_a_theorem(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.61  = { by axiom 1 (ifeq_axiom) }
% 168.80/24.61    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10)))))), true, is_a_theorem(equivalent(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, ifeq(is_a_theorem(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.62  = { by axiom 3 (lg_2) }
% 168.80/24.62    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, ifeq(is_a_theorem(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.62  = { by axiom 1 (ifeq_axiom) }
% 168.80/24.62    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(is_a_theorem(equivalent(W10, equivalent(W10, equivalent(equivalent(V10, U10), equivalent(equivalent(V10, T10), equivalent(U10, T10)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.63  = { by axiom 2 (condensed_detachment) }
% 168.80/24.63    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.63  = { by axiom 1 (ifeq_axiom) }
% 168.80/24.63    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.63  = { by axiom 1 (ifeq_axiom) R->L }
% 168.80/24.64    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.64  = { by axiom 2 (condensed_detachment) R->L }
% 168.80/24.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, ifeq(is_a_theorem(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.64  = { by axiom 1 (ifeq_axiom) R->L }
% 168.80/24.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, ifeq(is_a_theorem(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.65  = { by axiom 3 (lg_2) R->L }
% 168.80/24.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11)))))), true, is_a_theorem(equivalent(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, ifeq(is_a_theorem(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.65  = { by axiom 1 (ifeq_axiom) R->L }
% 168.80/24.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11)))))), true, is_a_theorem(equivalent(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, ifeq(is_a_theorem(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.66  = { by axiom 3 (lg_2) R->L }
% 168.80/24.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11))))), equivalent(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))))), true, ifeq(is_a_theorem(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11)))))), true, is_a_theorem(equivalent(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, ifeq(is_a_theorem(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.66  = { by axiom 2 (condensed_detachment) }
% 168.80/24.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.67  = { by axiom 1 (ifeq_axiom) }
% 168.80/24.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(S10, equivalent(S10, equivalent(equivalent(X11, Y11), equivalent(equivalent(X11, Z11), equivalent(Y11, Z11)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.67  = { by axiom 3 (lg_2) }
% 168.80/24.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.68  = { by axiom 1 (ifeq_axiom) }
% 168.80/24.68    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.69  = { by axiom 1 (ifeq_axiom) R->L }
% 168.80/24.69    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 168.80/24.69  = { by axiom 2 (condensed_detachment) R->L }
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% 169.49/24.70  = { by axiom 1 (ifeq_axiom) R->L }
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% 169.49/24.71  = { by axiom 3 (lg_2) R->L }
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% 169.49/24.72  = { by axiom 1 (ifeq_axiom) R->L }
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% 169.49/24.73  = { by axiom 3 (lg_2) R->L }
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% 169.49/24.74  = { by axiom 2 (condensed_detachment) }
% 169.49/24.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(W11, equivalent(W11, equivalent(equivalent(V11, U11), equivalent(equivalent(V11, T11), equivalent(U11, T11)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 169.49/24.75  = { by axiom 1 (ifeq_axiom) }
% 169.49/24.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(W11, equivalent(W11, equivalent(equivalent(V11, U11), equivalent(equivalent(V11, T11), equivalent(U11, T11)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 169.49/24.75  = { by axiom 3 (lg_2) }
% 169.49/24.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 169.49/24.76  = { by axiom 1 (ifeq_axiom) }
% 169.49/24.76    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(a, equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 169.49/24.76  = { by axiom 2 (condensed_detachment) }
% 169.49/24.76    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 169.49/24.76  = { by axiom 1 (ifeq_axiom) }
% 169.49/24.76    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(b, c), equivalent(equivalent(b, f), equivalent(c, f)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(equivalent(b, f), equivalent(c, f))), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 169.49/24.76  = { by axiom 2 (condensed_detachment) }
% 169.49/24.76    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 169.49/24.77  = { by axiom 1 (ifeq_axiom) }
% 169.49/24.77    ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true)
% 169.49/24.77  = { by axiom 1 (ifeq_axiom) R->L }
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% 169.49/24.77  = { by axiom 2 (condensed_detachment) R->L }
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% 169.49/24.78  = { by axiom 1 (ifeq_axiom) R->L }
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% 169.49/24.79  = { by axiom 2 (condensed_detachment) R->L }
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% 170.18/24.80  = { by axiom 1 (ifeq_axiom) R->L }
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% 170.18/24.82  = { by axiom 3 (lg_2) R->L }
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% 170.18/24.83  = { by axiom 1 (ifeq_axiom) R->L }
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% 170.18/24.85  = { by axiom 2 (condensed_detachment) R->L }
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% 170.92/24.91  = { by axiom 1 (ifeq_axiom) }
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% 170.92/24.91  = { by axiom 1 (ifeq_axiom) R->L }
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% 170.92/24.92  = { by axiom 3 (lg_2) R->L }
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% 170.92/24.92  = { by axiom 1 (ifeq_axiom) R->L }
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% 170.92/24.93  = { by axiom 2 (condensed_detachment) R->L }
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% 170.92/24.94  = { by axiom 3 (lg_2) }
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% 170.92/24.94  = { by axiom 1 (ifeq_axiom) }
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% 170.92/24.94  = { by axiom 3 (lg_2) }
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% 170.92/24.95  = { by axiom 1 (ifeq_axiom) }
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% 170.92/24.96  = { by axiom 2 (condensed_detachment) }
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% 170.92/24.96  = { by axiom 1 (ifeq_axiom) }
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% 170.92/24.96  = { by axiom 1 (ifeq_axiom) R->L }
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% 170.92/24.97  = { by axiom 2 (condensed_detachment) R->L }
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% 170.92/24.97  = { by axiom 1 (ifeq_axiom) R->L }
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% 170.92/24.98  = { by axiom 3 (lg_2) R->L }
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% 170.92/24.98  = { by axiom 1 (ifeq_axiom) R->L }
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% 170.92/24.99  = { by axiom 3 (lg_2) R->L }
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% 170.92/24.99  = { by axiom 2 (condensed_detachment) }
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% 170.92/25.00  = { by axiom 1 (ifeq_axiom) }
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% 170.92/25.00  = { by axiom 3 (lg_2) }
% 170.92/25.00    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true)
% 170.92/25.00  = { by axiom 1 (ifeq_axiom) }
% 170.92/25.01    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true)
% 170.92/25.01  = { by axiom 2 (condensed_detachment) }
% 170.92/25.01    ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true)
% 170.92/25.01  = { by axiom 1 (ifeq_axiom) }
% 170.92/25.01    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true)
% 170.92/25.01  = { by axiom 1 (ifeq_axiom) R->L }
% 170.92/25.01    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true)
% 170.92/25.01  = { by axiom 3 (lg_2) R->L }
% 170.92/25.01    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true)
% 170.92/25.01  = { by axiom 1 (ifeq_axiom) R->L }
% 170.92/25.01    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true)
% 170.92/25.01  = { by axiom 3 (lg_2) R->L }
% 170.92/25.01    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(equivalent(e, equivalent(b, f)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true)
% 170.92/25.01  = { by axiom 2 (condensed_detachment) }
% 170.92/25.01    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true)
% 170.92/25.01  = { by axiom 1 (ifeq_axiom) }
% 170.92/25.01    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f)))), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(e, equivalent(c, f)), equivalent(equivalent(b, f), equivalent(c, f)))), equivalent(a, equivalent(e, equivalent(c, f))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(e, equivalent(b, f))), equivalent(a, equivalent(e, equivalent(c, f))))), true), true)
% 170.92/25.01  = { by axiom 2 (condensed_detachment) }
% 170.92/25.01    true
% 170.92/25.01  % SZS output end Proof
% 170.92/25.01  
% 170.92/25.01  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------