Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL101-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n011.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 11:49:02 AM UTC 2026

% Result   : Unsatisfiable 0.64s 0.53s
% Output   : Proof 30.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL101-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34  % Computer : n011.cluster.edu
% 0.09/0.34  % Model    : x86_64 x86_64
% 0.09/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34  % Memory   : 8046.5625MB
% 0.09/0.34  % OS       : Linux 6.8.0-71-generic
% 0.09/0.34  % CPULimit : 300
% 0.09/0.34  % WCLimit  : 300
% 0.09/0.34  % DateTime : Sun Sep 27 15:21:30 UTC 2026
% 0.09/0.35  % CPUTime  : 
% 0.09/0.35  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.64/0.53  Command-line arguments: --no-flatten-goal
% 0.64/0.53  
% 0.64/0.53  % SZS status Unsatisfiable
% 0.64/0.53  
% 13.94/2.47  % SZS output start Proof
% 13.94/2.47  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 13.94/2.47  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.
% 13.94/2.47  Axiom 3 (p_4): is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, W)), equivalent(Z, W)), X))) = true.
% 14.65/2.51  Axiom 4 (lg_2): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)) = true.
% 14.65/2.51  
% 14.65/2.51  Goal 1 (prove_p_1): is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))) = true.
% 14.65/2.51  Proof:
% 14.65/2.51    is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 14.65/2.51  = { by axiom 1 (ifeq_axiom) R->L }
% 14.65/2.51    ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 14.65/2.51  = { by axiom 2 (condensed_detachment) R->L }
% 14.65/2.51    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 14.65/2.51  = { by axiom 3 (p_4) }
% 14.65/2.51    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 14.65/2.52  = { by axiom 1 (ifeq_axiom) }
% 14.65/2.52    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 14.65/2.53  = { by axiom 1 (ifeq_axiom) R->L }
% 14.65/2.53    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 14.65/2.54  = { by axiom 2 (condensed_detachment) R->L }
% 14.65/2.55    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 14.65/2.56  = { by axiom 1 (ifeq_axiom) R->L }
% 14.65/2.56    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 14.65/2.57  = { by axiom 2 (condensed_detachment) R->L }
% 14.65/2.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 15.35/2.60  = { by axiom 4 (lg_2) }
% 15.35/2.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 15.35/2.61  = { by axiom 1 (ifeq_axiom) }
% 15.35/2.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 15.35/2.63  = { by axiom 3 (p_4) }
% 15.35/2.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 15.35/2.65  = { by axiom 1 (ifeq_axiom) }
% 15.35/2.66    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 15.35/2.66  = { by axiom 1 (ifeq_axiom) R->L }
% 15.35/2.66    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 15.35/2.67  = { by axiom 4 (lg_2) R->L }
% 15.35/2.68    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 15.35/2.68  = { by axiom 2 (condensed_detachment) }
% 15.35/2.69    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 15.35/2.69  = { by axiom 1 (ifeq_axiom) }
% 15.35/2.69    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 16.05/2.70  = { by axiom 1 (ifeq_axiom) R->L }
% 16.05/2.70    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 16.05/2.72  = { by axiom 2 (condensed_detachment) R->L }
% 16.05/2.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 16.05/2.74  = { by axiom 1 (ifeq_axiom) R->L }
% 16.05/2.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 16.05/2.76  = { by axiom 2 (condensed_detachment) R->L }
% 16.05/2.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(V, U), equivalent(V, T)), equivalent(U, T)), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(equivalent(equivalent(V, U), equivalent(V, T)), equivalent(U, T)), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(V, U), equivalent(V, T)), equivalent(U, T)), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(V, U), equivalent(V, T)), equivalent(U, T)), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 16.05/2.79  = { by axiom 4 (lg_2) }
% 16.05/2.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(V, U), equivalent(V, T)), equivalent(U, T)), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(V, U), equivalent(V, T)), equivalent(U, T)), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 16.77/2.81  = { by axiom 1 (ifeq_axiom) }
% 16.77/2.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(V, U), equivalent(V, T)), equivalent(U, T)), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(V, U), equivalent(V, T)), equivalent(U, T)), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 16.77/2.83  = { by axiom 3 (p_4) }
% 16.77/2.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(V, U), equivalent(V, T)), equivalent(U, T)), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 16.77/2.84  = { by axiom 1 (ifeq_axiom) }
% 16.77/2.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(V, U), equivalent(V, T)), equivalent(U, T)), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 16.77/2.85  = { by axiom 1 (ifeq_axiom) R->L }
% 16.77/2.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(V, U), equivalent(V, T)), equivalent(U, T)), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 16.77/2.87  = { by axiom 4 (lg_2) R->L }
% 16.77/2.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(V, U), equivalent(V, T)), equivalent(U, T)), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(V, U), equivalent(V, T)), equivalent(U, T)), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 16.77/2.88  = { by axiom 2 (condensed_detachment) }
% 16.77/2.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 17.45/2.90  = { by axiom 1 (ifeq_axiom) }
% 17.45/2.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 17.45/2.91  = { by axiom 1 (ifeq_axiom) R->L }
% 17.45/2.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 17.45/2.92  = { by axiom 2 (condensed_detachment) R->L }
% 17.45/2.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 17.45/2.94  = { by axiom 4 (lg_2) }
% 17.45/2.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 17.45/2.96  = { by axiom 1 (ifeq_axiom) }
% 17.45/2.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 17.45/2.98  = { by axiom 3 (p_4) }
% 17.45/2.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 17.45/3.00  = { by axiom 1 (ifeq_axiom) }
% 17.45/3.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 17.45/3.03  = { by axiom 1 (ifeq_axiom) R->L }
% 17.45/3.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 18.38/3.04  = { by axiom 2 (condensed_detachment) R->L }
% 18.38/3.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 18.38/3.08  = { by axiom 4 (lg_2) }
% 18.38/3.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 18.38/3.11  = { by axiom 1 (ifeq_axiom) }
% 18.38/3.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 19.12/3.15  = { by axiom 1 (ifeq_axiom) R->L }
% 19.12/3.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 19.12/3.19  = { by axiom 3 (p_4) R->L }
% 19.59/3.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 19.59/3.22  = { by axiom 1 (ifeq_axiom) R->L }
% 19.59/3.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 19.59/3.25  = { by axiom 4 (lg_2) R->L }
% 19.59/3.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), equivalent(Y2, Z2)), equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 19.59/3.29  = { by axiom 2 (condensed_detachment) }
% 20.29/3.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 20.29/3.30  = { by axiom 1 (ifeq_axiom) }
% 20.29/3.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(S, W), equivalent(S, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(W, equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 20.29/3.31  = { by axiom 2 (condensed_detachment) }
% 20.29/3.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 20.29/3.32  = { by axiom 1 (ifeq_axiom) }
% 20.29/3.32    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 20.29/3.32  = { by axiom 1 (ifeq_axiom) R->L }
% 20.29/3.33    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 20.29/3.33  = { by axiom 3 (p_4) R->L }
% 20.29/3.33    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 20.29/3.33  = { by axiom 2 (condensed_detachment) }
% 20.29/3.34    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 20.29/3.34  = { by axiom 1 (ifeq_axiom) }
% 20.29/3.34    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 20.29/3.34  = { by axiom 1 (ifeq_axiom) R->L }
% 20.29/3.34    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 20.29/3.34  = { by axiom 4 (lg_2) R->L }
% 20.29/3.34    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 20.29/3.34  = { by axiom 2 (condensed_detachment) }
% 20.29/3.34    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 20.29/3.34  = { by axiom 1 (ifeq_axiom) }
% 20.29/3.34    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 20.29/3.34  = { by axiom 1 (ifeq_axiom) R->L }
% 20.29/3.34    ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 20.29/3.34  = { by axiom 2 (condensed_detachment) R->L }
% 20.29/3.35    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 20.29/3.35  = { by axiom 3 (p_4) }
% 20.29/3.35    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 20.29/3.36  = { by axiom 1 (ifeq_axiom) }
% 20.29/3.36    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 20.29/3.37  = { by axiom 1 (ifeq_axiom) R->L }
% 20.29/3.38    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 20.99/3.41  = { by axiom 2 (condensed_detachment) R->L }
% 20.99/3.42    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 20.99/3.44  = { by axiom 1 (ifeq_axiom) R->L }
% 20.99/3.45    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 20.99/3.47  = { by axiom 2 (condensed_detachment) R->L }
% 21.71/3.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(W2, V2), equivalent(W2, U2)), equivalent(V2, U2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), equivalent(equivalent(equivalent(equivalent(W2, V2), equivalent(W2, U2)), equivalent(V2, U2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(W2, V2), equivalent(W2, U2)), equivalent(V2, U2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(W2, V2), equivalent(W2, U2)), equivalent(V2, U2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 21.71/3.51  = { by axiom 4 (lg_2) }
% 21.71/3.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(W2, V2), equivalent(W2, U2)), equivalent(V2, U2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(W2, V2), equivalent(W2, U2)), equivalent(V2, U2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 21.71/3.54  = { by axiom 1 (ifeq_axiom) }
% 21.71/3.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(W2, V2), equivalent(W2, U2)), equivalent(V2, U2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(W2, V2), equivalent(W2, U2)), equivalent(V2, U2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 21.71/3.58  = { by axiom 3 (p_4) }
% 21.71/3.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(W2, V2), equivalent(W2, U2)), equivalent(V2, U2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 22.41/3.61  = { by axiom 1 (ifeq_axiom) }
% 22.41/3.62    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W2, V2), equivalent(W2, U2)), equivalent(V2, U2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 22.41/3.63  = { by axiom 1 (ifeq_axiom) R->L }
% 22.41/3.64    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W2, V2), equivalent(W2, U2)), equivalent(V2, U2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 22.41/3.64  = { by axiom 4 (lg_2) R->L }
% 22.41/3.66    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(W2, V2), equivalent(W2, U2)), equivalent(V2, U2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W2, V2), equivalent(W2, U2)), equivalent(V2, U2)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 22.41/3.67  = { by axiom 2 (condensed_detachment) }
% 22.41/3.67    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 22.41/3.68  = { by axiom 1 (ifeq_axiom) }
% 22.41/3.68    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 23.13/3.70  = { by axiom 1 (ifeq_axiom) R->L }
% 23.13/3.71    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 23.13/3.74  = { by axiom 2 (condensed_detachment) R->L }
% 23.13/3.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 23.13/3.77  = { by axiom 1 (ifeq_axiom) R->L }
% 23.13/3.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 23.83/3.80  = { by axiom 2 (condensed_detachment) R->L }
% 23.83/3.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(S2, X3), equivalent(S2, Y3)), equivalent(X3, Y3)), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), equivalent(equivalent(equivalent(equivalent(S2, X3), equivalent(S2, Y3)), equivalent(X3, Y3)), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(S2, X3), equivalent(S2, Y3)), equivalent(X3, Y3)), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(S2, X3), equivalent(S2, Y3)), equivalent(X3, Y3)), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 23.83/3.85  = { by axiom 4 (lg_2) }
% 23.83/3.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(S2, X3), equivalent(S2, Y3)), equivalent(X3, Y3)), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(S2, X3), equivalent(S2, Y3)), equivalent(X3, Y3)), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 23.83/3.88  = { by axiom 1 (ifeq_axiom) }
% 24.52/3.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(S2, X3), equivalent(S2, Y3)), equivalent(X3, Y3)), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(S2, X3), equivalent(S2, Y3)), equivalent(X3, Y3)), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 24.52/3.92  = { by axiom 3 (p_4) }
% 24.52/3.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(S2, X3), equivalent(S2, Y3)), equivalent(X3, Y3)), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 24.52/3.95  = { by axiom 1 (ifeq_axiom) }
% 24.52/3.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S2, X3), equivalent(S2, Y3)), equivalent(X3, Y3)), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 24.52/3.97  = { by axiom 1 (ifeq_axiom) R->L }
% 24.52/3.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S2, X3), equivalent(S2, Y3)), equivalent(X3, Y3)), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 24.52/3.99  = { by axiom 4 (lg_2) R->L }
% 24.52/4.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(S2, X3), equivalent(S2, Y3)), equivalent(X3, Y3)), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S2, X3), equivalent(S2, Y3)), equivalent(X3, Y3)), equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 24.52/4.03  = { by axiom 2 (condensed_detachment) }
% 25.45/4.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 25.45/4.06  = { by axiom 1 (ifeq_axiom) }
% 25.45/4.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 25.45/4.08  = { by axiom 1 (ifeq_axiom) R->L }
% 25.45/4.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 25.45/4.11  = { by axiom 2 (condensed_detachment) R->L }
% 26.15/4.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 26.15/4.14  = { by axiom 4 (lg_2) }
% 26.15/4.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 26.15/4.17  = { by axiom 1 (ifeq_axiom) }
% 26.15/4.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 26.64/4.21  = { by axiom 3 (p_4) }
% 26.64/4.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 26.64/4.25  = { by axiom 1 (ifeq_axiom) }
% 26.64/4.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 26.64/4.29  = { by axiom 1 (ifeq_axiom) R->L }
% 27.35/4.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 27.35/4.32  = { by axiom 2 (condensed_detachment) R->L }
% 27.35/4.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(W3, V3), equivalent(W3, U3)), equivalent(V3, U3)), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W3, V3), equivalent(W3, U3)), equivalent(V3, U3)), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 27.35/4.39  = { by axiom 4 (lg_2) }
% 28.04/4.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W3, V3), equivalent(W3, U3)), equivalent(V3, U3)), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 28.04/4.46  = { by axiom 1 (ifeq_axiom) }
% 28.04/4.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W3, V3), equivalent(W3, U3)), equivalent(V3, U3)), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 28.75/4.54  = { by axiom 1 (ifeq_axiom) R->L }
% 28.75/4.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(W3, V3), equivalent(W3, U3)), equivalent(V3, U3)), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 29.46/4.62  = { by axiom 3 (p_4) R->L }
% 29.46/4.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(equivalent(equivalent(W3, V3), equivalent(W3, U3)), equivalent(V3, U3)), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(W3, V3), equivalent(W3, U3)), equivalent(V3, U3)), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 29.46/4.68  = { by axiom 1 (ifeq_axiom) R->L }
% 30.15/4.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(equivalent(equivalent(W3, V3), equivalent(W3, U3)), equivalent(V3, U3)), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(W3, V3), equivalent(W3, U3)), equivalent(V3, U3)), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.15/4.73  = { by axiom 4 (lg_2) R->L }
% 30.15/4.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(equivalent(equivalent(W3, V3), equivalent(W3, U3)), equivalent(V3, U3)), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), equivalent(equivalent(equivalent(equivalent(W3, V3), equivalent(W3, U3)), equivalent(V3, U3)), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(equivalent(equivalent(W3, V3), equivalent(W3, U3)), equivalent(V3, U3)), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(W3, V3), equivalent(W3, U3)), equivalent(V3, U3)), equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.15/4.79  = { by axiom 2 (condensed_detachment) }
% 30.87/4.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.87/4.81  = { by axiom 1 (ifeq_axiom) }
% 30.87/4.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(Z3, T2), equivalent(Z3, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(T2, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.87/4.83  = { by axiom 2 (condensed_detachment) }
% 30.87/4.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.87/4.84  = { by axiom 1 (ifeq_axiom) }
% 30.87/4.84    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.87/4.84  = { by axiom 1 (ifeq_axiom) R->L }
% 30.87/4.85    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.87/4.85  = { by axiom 3 (p_4) R->L }
% 30.87/4.86    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.87/4.86  = { by axiom 2 (condensed_detachment) }
% 30.87/4.86    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.87/4.87  = { by axiom 1 (ifeq_axiom) }
% 30.87/4.87    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.87/4.87  = { by axiom 1 (ifeq_axiom) R->L }
% 30.87/4.87    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.87/4.87  = { by axiom 4 (lg_2) R->L }
% 30.87/4.87    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.87/4.87  = { by axiom 2 (condensed_detachment) }
% 30.87/4.87    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.87/4.87  = { by axiom 1 (ifeq_axiom) }
% 30.87/4.88    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 30.87/4.88  = { by axiom 2 (condensed_detachment) }
% 30.87/4.88    true
% 30.87/4.88  % SZS output end Proof
% 30.87/4.88  
% 30.87/4.88  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------