Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL097-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n019.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 11:49:01 AM UTC 2026

% Result   : Unsatisfiable 56.90s 7.69s
% Output   : Proof 75.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL097-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36  % Computer : n019.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.37  % CPULimit : 300
% 0.09/0.37  % WCLimit  : 300
% 0.09/0.37  % DateTime : Sun Sep 27 15:21:48 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.37  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 56.90/7.69  Command-line arguments: --flatten-regeneralise
% 56.90/7.69  
% 56.90/7.69  % SZS status Unsatisfiable
% 56.90/7.69  
% 67.22/8.93  % SZS output start Proof
% 67.22/8.93  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 67.22/8.93  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.
% 67.22/8.93  Axiom 3 (lg_2): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)) = true.
% 67.22/8.95  Axiom 4 (lg_3): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V), V)) = true.
% 67.22/8.95  
% 67.22/8.96  Goal 1 (prove_lg_4): is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))) = true.
% 67.22/8.96  Proof:
% 67.22/8.96    is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 67.22/8.96  = { by axiom 1 (ifeq_axiom) R->L }
% 67.22/8.96    ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 67.22/8.97  = { by axiom 2 (condensed_detachment) R->L }
% 67.22/8.97    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 67.22/8.97  = { by axiom 1 (ifeq_axiom) R->L }
% 67.22/8.97    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 67.22/9.00  = { by axiom 4 (lg_3) R->L }
% 67.22/9.00    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 67.22/9.02  = { by axiom 1 (ifeq_axiom) R->L }
% 67.22/9.02    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 67.22/9.04  = { by axiom 2 (condensed_detachment) R->L }
% 68.29/9.06    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(X, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(X, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 68.29/9.06  = { by axiom 3 (lg_2) }
% 68.29/9.07    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(X, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 68.29/9.08  = { by axiom 1 (ifeq_axiom) }
% 68.29/9.09    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(X, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), 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falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 68.29/9.09  = { by axiom 4 (lg_3) }
% 68.29/9.10    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 68.29/9.10  = { by axiom 1 (ifeq_axiom) }
% 68.29/9.10    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 68.29/9.11  = { by axiom 2 (condensed_detachment) }
% 68.29/9.11    ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 68.29/9.11  = { by axiom 1 (ifeq_axiom) }
% 68.29/9.11    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 68.29/9.12  = { by axiom 1 (ifeq_axiom) R->L }
% 68.29/9.12    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 68.29/9.13  = { by axiom 4 (lg_3) R->L }
% 68.29/9.13    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 68.29/9.14  = { by axiom 1 (ifeq_axiom) R->L }
% 69.12/9.14    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 69.12/9.15  = { by axiom 2 (condensed_detachment) R->L }
% 69.12/9.16    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(Y, equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(Y, equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 69.12/9.16  = { by axiom 3 (lg_2) }
% 69.12/9.17    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(Y, equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 69.12/9.17  = { by axiom 1 (ifeq_axiom) }
% 69.12/9.18    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(Y, equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 69.12/9.18  = { by axiom 4 (lg_3) }
% 69.12/9.19    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 69.12/9.19  = { by axiom 1 (ifeq_axiom) }
% 69.12/9.19    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 69.12/9.19  = { by axiom 2 (condensed_detachment) }
% 69.12/9.19    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 69.12/9.19  = { by axiom 1 (ifeq_axiom) }
% 69.12/9.19    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true)
% 69.12/9.19  = { by axiom 1 (ifeq_axiom) R->L }
% 69.12/9.19    ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 69.58/9.21  = { by axiom 2 (condensed_detachment) R->L }
% 69.58/9.21    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 69.58/9.24  = { by axiom 1 (ifeq_axiom) R->L }
% 69.58/9.24    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 70.41/9.32  = { by axiom 2 (condensed_detachment) R->L }
% 70.41/9.34    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), 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% 71.19/9.43  = { by axiom 1 (ifeq_axiom) R->L }
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% 71.19/9.48  = { by axiom 4 (lg_3) R->L }
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% 72.03/9.53  = { by axiom 1 (ifeq_axiom) R->L }
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% 72.03/9.58  = { by axiom 3 (lg_2) R->L }
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equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 72.79/9.63  = { by axiom 2 (condensed_detachment) }
% 72.79/9.64    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 72.79/9.64  = { by axiom 1 (ifeq_axiom) }
% 72.79/9.65    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 72.79/9.66  = { by axiom 4 (lg_3) }
% 72.79/9.66    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 72.79/9.67  = { by axiom 1 (ifeq_axiom) }
% 72.79/9.68    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 72.79/9.69  = { by axiom 1 (ifeq_axiom) R->L }
% 72.79/9.70    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 72.79/9.70  = { by axiom 2 (condensed_detachment) R->L }
% 73.60/9.72    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(W, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, 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c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 73.60/9.72  = { by axiom 3 (lg_2) }
% 73.60/9.73    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(W, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), 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equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 73.60/9.73  = { by axiom 1 (ifeq_axiom) }
% 73.60/9.74    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), equivalent(W, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), 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equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 73.60/9.74  = { by axiom 4 (lg_3) }
% 73.60/9.74    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 73.60/9.74  = { by axiom 1 (ifeq_axiom) }
% 73.60/9.75    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 73.60/9.75  = { by axiom 2 (condensed_detachment) }
% 73.60/9.75    ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 73.60/9.75  = { by axiom 1 (ifeq_axiom) }
% 73.60/9.76    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 73.60/9.76  = { by axiom 1 (ifeq_axiom) R->L }
% 73.60/9.76    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 73.60/9.77  = { by axiom 2 (condensed_detachment) R->L }
% 73.60/9.77    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 73.60/9.78  = { by axiom 1 (ifeq_axiom) R->L }
% 73.60/9.78    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 73.60/9.79  = { by axiom 4 (lg_3) R->L }
% 73.60/9.79    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(V, equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(V, equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 73.60/9.80  = { by axiom 1 (ifeq_axiom) R->L }
% 73.60/9.80    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(V, equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(V, equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 73.60/9.80  = { by axiom 3 (lg_2) R->L }
% 74.43/9.80    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(V, equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(V, equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, 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equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(V, equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, 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ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 74.43/9.81  = { by axiom 2 (condensed_detachment) }
% 74.43/9.81    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 74.43/9.81  = { by axiom 1 (ifeq_axiom) }
% 74.43/9.81    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 74.43/9.82  = { by axiom 1 (ifeq_axiom) R->L }
% 74.43/9.83    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 74.43/9.85  = { by axiom 4 (lg_3) R->L }
% 74.43/9.86    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 74.43/9.88  = { by axiom 1 (ifeq_axiom) R->L }
% 74.43/9.88    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 74.43/9.90  = { by axiom 2 (condensed_detachment) R->L }
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% 75.22/9.92  = { by axiom 3 (lg_2) }
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% 75.22/9.94  = { by axiom 1 (ifeq_axiom) }
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falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 75.22/9.95  = { by axiom 4 (lg_3) }
% 75.22/9.96    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 75.22/9.96  = { by axiom 1 (ifeq_axiom) }
% 75.22/9.96    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 75.22/9.96  = { by axiom 2 (condensed_detachment) }
% 75.22/9.96    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 75.22/9.96  = { by axiom 1 (ifeq_axiom) }
% 75.22/9.97    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 75.22/9.97  = { by axiom 1 (ifeq_axiom) R->L }
% 75.22/9.97    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 75.22/9.97  = { by axiom 4 (lg_3) R->L }
% 75.22/9.97    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 75.22/9.97  = { by axiom 2 (condensed_detachment) }
% 75.22/9.97    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 75.22/9.97  = { by axiom 1 (ifeq_axiom) }
% 75.22/9.97    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true), true)
% 75.22/9.97  = { by axiom 2 (condensed_detachment) }
% 75.22/9.97    true
% 75.22/9.97  % SZS output end Proof
% 75.22/9.97  
% 75.22/9.97  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------