Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL257-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n007.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 11:49:30 AM UTC 2026

% Result   : Unsatisfiable 0.29s 1.01s
% Output   : Proof 21.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : LCL257-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45  % Computer : n007.cluster.edu
% 0.19/0.45  % Model    : x86_64 x86_64
% 0.19/0.45  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45  % Memory   : 8046.5625MB
% 0.19/0.45  % OS       : Linux 6.8.0-71-generic
% 0.19/0.45  % CPULimit : 300
% 0.19/0.45  % WCLimit  : 300
% 0.19/0.45  % DateTime : Sun Sep 27 15:29:24 UTC 2026
% 0.19/0.46  % CPUTime  : 
% 0.19/0.46  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.29/1.01  Command-line arguments: --no-flatten-goal
% 0.29/1.01  
% 0.29/1.01  % SZS status Unsatisfiable
% 0.29/1.01  
% 15.39/3.02  % SZS output start Proof
% 15.39/3.02  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 15.39/3.02  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.
% 16.00/3.07  Axiom 3 (yql): is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, Y), equivalent(X, Z)))) = true.
% 16.00/3.07  
% 16.00/3.07  Goal 1 (prove_xhn): is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))) = true.
% 16.00/3.07  Proof:
% 16.00/3.07    is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 16.00/3.07  = { by axiom 1 (ifeq_axiom) R->L }
% 16.00/3.07    ifeq(true, true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.07  = { by axiom 2 (condensed_detachment) R->L }
% 16.00/3.07    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.07  = { by axiom 3 (yql) }
% 16.00/3.07    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.07  = { by axiom 1 (ifeq_axiom) }
% 16.00/3.07    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.07  = { by axiom 1 (ifeq_axiom) R->L }
% 16.00/3.07    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.07  = { by axiom 2 (condensed_detachment) R->L }
% 16.00/3.07    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.07  = { by axiom 3 (yql) }
% 16.00/3.07    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.08  = { by axiom 1 (ifeq_axiom) }
% 16.00/3.08    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.08  = { by axiom 1 (ifeq_axiom) R->L }
% 16.00/3.08    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.08  = { by axiom 2 (condensed_detachment) R->L }
% 16.00/3.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.09  = { by axiom 1 (ifeq_axiom) R->L }
% 16.00/3.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.09  = { by axiom 2 (condensed_detachment) R->L }
% 16.00/3.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.10  = { by axiom 1 (ifeq_axiom) R->L }
% 16.00/3.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.10  = { by axiom 2 (condensed_detachment) R->L }
% 16.00/3.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(X, equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), X))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(X, equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), X))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(X, equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(X, equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), X))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.12  = { by axiom 3 (yql) }
% 16.00/3.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(X, equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(X, equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), X))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.12  = { by axiom 1 (ifeq_axiom) }
% 16.00/3.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(X, equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(X, equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), X))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.13  = { by axiom 3 (yql) }
% 16.00/3.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(X, equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), X))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.13  = { by axiom 1 (ifeq_axiom) }
% 16.00/3.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(X, equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), X))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.14  = { by axiom 1 (ifeq_axiom) R->L }
% 16.00/3.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(X, equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), X))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.14  = { by axiom 3 (yql) R->L }
% 16.00/3.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(X, equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), X))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(X, equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.15  = { by axiom 2 (condensed_detachment) }
% 16.00/3.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.00/3.15  = { by axiom 1 (ifeq_axiom) }
% 16.55/3.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.55/3.16  = { by axiom 1 (ifeq_axiom) R->L }
% 16.55/3.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.55/3.16  = { by axiom 2 (condensed_detachment) R->L }
% 16.55/3.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.55/3.17  = { by axiom 3 (yql) }
% 16.55/3.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.55/3.18  = { by axiom 1 (ifeq_axiom) }
% 16.55/3.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.55/3.19  = { by axiom 1 (ifeq_axiom) R->L }
% 16.55/3.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.55/3.19  = { by axiom 2 (condensed_detachment) R->L }
% 16.55/3.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.55/3.21  = { by axiom 3 (yql) }
% 16.55/3.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.55/3.22  = { by axiom 1 (ifeq_axiom) }
% 16.55/3.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.55/3.23  = { by axiom 3 (yql) }
% 16.55/3.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.55/3.24  = { by axiom 1 (ifeq_axiom) }
% 16.55/3.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 16.55/3.24  = { by axiom 1 (ifeq_axiom) R->L }
% 16.55/3.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.20/3.25  = { by axiom 3 (yql) R->L }
% 17.20/3.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.20/3.26  = { by axiom 2 (condensed_detachment) }
% 17.20/3.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.20/3.27  = { by axiom 1 (ifeq_axiom) }
% 17.20/3.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.20/3.27  = { by axiom 1 (ifeq_axiom) R->L }
% 17.20/3.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.20/3.27  = { by axiom 3 (yql) R->L }
% 17.20/3.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.20/3.28  = { by axiom 2 (condensed_detachment) }
% 17.20/3.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.20/3.28  = { by axiom 1 (ifeq_axiom) }
% 17.20/3.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.20/3.28  = { by axiom 1 (ifeq_axiom) R->L }
% 17.20/3.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.20/3.29  = { by axiom 3 (yql) R->L }
% 17.20/3.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.20/3.29  = { by axiom 2 (condensed_detachment) }
% 17.20/3.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.20/3.29  = { by axiom 1 (ifeq_axiom) }
% 17.20/3.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.20/3.29  = { by axiom 1 (ifeq_axiom) R->L }
% 17.20/3.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.20/3.30  = { by axiom 2 (condensed_detachment) R->L }
% 17.48/3.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.30  = { by axiom 3 (yql) }
% 17.48/3.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.31  = { by axiom 1 (ifeq_axiom) }
% 17.48/3.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.31  = { by axiom 1 (ifeq_axiom) R->L }
% 17.48/3.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.32  = { by axiom 2 (condensed_detachment) R->L }
% 17.48/3.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.32  = { by axiom 1 (ifeq_axiom) R->L }
% 17.48/3.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.33  = { by axiom 2 (condensed_detachment) R->L }
% 17.48/3.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(Z, equivalent(z, x)), equivalent(equivalent(z, x), Z))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(Z, equivalent(z, x)), equivalent(equivalent(z, x), Z))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(Z, equivalent(z, x)), equivalent(equivalent(z, x), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(Z, equivalent(z, x)), equivalent(equivalent(z, x), Z))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.33  = { by axiom 3 (yql) }
% 17.48/3.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(Z, equivalent(z, x)), equivalent(equivalent(z, x), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(Z, equivalent(z, x)), equivalent(equivalent(z, x), Z))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.34  = { by axiom 1 (ifeq_axiom) }
% 17.48/3.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(Z, equivalent(z, x)), equivalent(equivalent(z, x), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(Z, equivalent(z, x)), equivalent(equivalent(z, x), Z))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.35  = { by axiom 3 (yql) }
% 17.48/3.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(Z, equivalent(z, x)), equivalent(equivalent(z, x), Z))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.35  = { by axiom 1 (ifeq_axiom) }
% 17.48/3.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(Z, equivalent(z, x)), equivalent(equivalent(z, x), Z))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.36  = { by axiom 1 (ifeq_axiom) R->L }
% 17.48/3.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(Z, equivalent(z, x)), equivalent(equivalent(z, x), Z))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.36  = { by axiom 3 (yql) R->L }
% 17.48/3.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(Z, equivalent(z, x)), equivalent(equivalent(z, x), Z))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(Z, equivalent(z, x)), equivalent(equivalent(z, x), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.37  = { by axiom 2 (condensed_detachment) }
% 17.48/3.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.37  = { by axiom 1 (ifeq_axiom) }
% 17.48/3.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.38  = { by axiom 1 (ifeq_axiom) R->L }
% 17.48/3.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.38  = { by axiom 2 (condensed_detachment) R->L }
% 17.48/3.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 17.48/3.39  = { by axiom 3 (yql) }
% 17.48/3.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.40  = { by axiom 1 (ifeq_axiom) }
% 18.10/3.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.41  = { by axiom 1 (ifeq_axiom) R->L }
% 18.10/3.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.41  = { by axiom 2 (condensed_detachment) R->L }
% 18.10/3.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(W, equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), W))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(W, equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), W))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(W, equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), W)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(W, equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), W))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.42  = { by axiom 3 (yql) }
% 18.10/3.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(W, equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), W)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(W, equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), W))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.43  = { by axiom 1 (ifeq_axiom) }
% 18.10/3.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(W, equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), W)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(W, equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), W))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.44  = { by axiom 3 (yql) }
% 18.10/3.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(W, equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), W))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.45  = { by axiom 1 (ifeq_axiom) }
% 18.10/3.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(W, equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), W))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.45  = { by axiom 1 (ifeq_axiom) R->L }
% 18.10/3.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(W, equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), W))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.46  = { by axiom 3 (yql) R->L }
% 18.10/3.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(W, equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), W))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(W, equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), W)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.46  = { by axiom 2 (condensed_detachment) }
% 18.10/3.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.47  = { by axiom 1 (ifeq_axiom) }
% 18.10/3.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.47  = { by axiom 1 (ifeq_axiom) R->L }
% 18.10/3.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.48  = { by axiom 3 (yql) R->L }
% 18.10/3.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(z, x))), equivalent(equivalent(z, x), equivalent(z, x)))), true), true), true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.48  = { by axiom 2 (condensed_detachment) }
% 18.10/3.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.48  = { by axiom 1 (ifeq_axiom) }
% 18.10/3.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.48  = { by axiom 1 (ifeq_axiom) R->L }
% 18.10/3.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.49  = { by axiom 3 (yql) R->L }
% 18.10/3.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(z, x)), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))))), true, ifeq(is_a_theorem(equivalent(equivalent(z, x), equivalent(z, x))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.49  = { by axiom 2 (condensed_detachment) }
% 18.10/3.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.49  = { by axiom 1 (ifeq_axiom) }
% 18.10/3.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.49  = { by axiom 1 (ifeq_axiom) R->L }
% 18.10/3.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.50  = { by axiom 3 (yql) R->L }
% 18.10/3.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(z, x), equivalent(equivalent(z, x), z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)), equivalent(equivalent(z, x), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.10/3.50  = { by axiom 2 (condensed_detachment) }
% 18.10/3.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.50  = { by axiom 1 (ifeq_axiom) }
% 18.69/3.50    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.50  = { by axiom 1 (ifeq_axiom) R->L }
% 18.69/3.50    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.51  = { by axiom 2 (condensed_detachment) R->L }
% 18.69/3.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.51  = { by axiom 3 (yql) }
% 18.69/3.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.51  = { by axiom 1 (ifeq_axiom) }
% 18.69/3.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.52  = { by axiom 1 (ifeq_axiom) R->L }
% 18.69/3.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.52  = { by axiom 2 (condensed_detachment) R->L }
% 18.69/3.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(V, equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), V))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(V, equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), V)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.53  = { by axiom 3 (yql) }
% 18.69/3.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(V, equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), V))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.53  = { by axiom 1 (ifeq_axiom) }
% 18.69/3.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(V, equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), V))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.54  = { by axiom 1 (ifeq_axiom) R->L }
% 18.69/3.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(V, equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), V))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.54  = { by axiom 3 (yql) R->L }
% 18.69/3.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(V, equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), V)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(V, equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), V))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.55  = { by axiom 1 (ifeq_axiom) R->L }
% 18.69/3.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(V, equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), V)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(V, equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), V))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.55  = { by axiom 3 (yql) R->L }
% 18.69/3.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(V, equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), V))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(V, equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), V))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(V, equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), V)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(V, equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), V))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.56  = { by axiom 2 (condensed_detachment) }
% 18.69/3.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.56  = { by axiom 1 (ifeq_axiom) }
% 18.69/3.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.57  = { by axiom 1 (ifeq_axiom) R->L }
% 18.69/3.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.57  = { by axiom 3 (yql) R->L }
% 18.69/3.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), x), equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.58  = { by axiom 2 (condensed_detachment) }
% 18.69/3.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.58  = { by axiom 1 (ifeq_axiom) }
% 18.69/3.58    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x))), equivalent(equivalent(equivalent(z, x), z), x))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(z, x), x), equivalent(equivalent(equivalent(z, x), z), equivalent(z, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(z, x), z), x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.58  = { by axiom 2 (condensed_detachment) }
% 18.69/3.58    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.58  = { by axiom 1 (ifeq_axiom) }
% 18.69/3.58    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.58  = { by axiom 1 (ifeq_axiom) R->L }
% 18.69/3.58    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.58  = { by axiom 2 (condensed_detachment) R->L }
% 18.69/3.59    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.59  = { by axiom 3 (yql) }
% 18.69/3.59    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 18.69/3.60  = { by axiom 1 (ifeq_axiom) }
% 18.69/3.60    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 19.31/3.61  = { by axiom 1 (ifeq_axiom) R->L }
% 19.31/3.61    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 19.31/3.61  = { by axiom 2 (condensed_detachment) R->L }
% 19.31/3.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 19.31/3.62  = { by axiom 3 (yql) }
% 19.31/3.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 19.31/3.64  = { by axiom 1 (ifeq_axiom) }
% 19.31/3.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 19.31/3.66  = { by axiom 1 (ifeq_axiom) R->L }
% 19.31/3.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 19.31/3.67  = { by axiom 2 (condensed_detachment) R->L }
% 19.31/3.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(U, equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), 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% 19.90/3.71  = { by axiom 3 (yql) }
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% 19.90/3.73  = { by axiom 1 (ifeq_axiom) }
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% 19.90/3.75  = { by axiom 1 (ifeq_axiom) R->L }
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% 19.90/3.77  = { by axiom 3 (yql) R->L }
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% 19.90/3.79  = { by axiom 1 (ifeq_axiom) R->L }
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% 20.51/3.81  = { by axiom 3 (yql) R->L }
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% 20.51/3.83  = { by axiom 2 (condensed_detachment) }
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% 20.51/3.84  = { by axiom 1 (ifeq_axiom) }
% 20.51/3.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 20.51/3.85  = { by axiom 1 (ifeq_axiom) R->L }
% 20.51/3.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 20.51/3.86  = { by axiom 3 (yql) R->L }
% 20.51/3.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), 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equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), 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is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 20.51/3.88  = { by axiom 2 (condensed_detachment) }
% 20.51/3.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 20.51/3.89  = { by axiom 1 (ifeq_axiom) }
% 20.51/3.89    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 20.51/3.90  = { by axiom 1 (ifeq_axiom) R->L }
% 20.51/3.90    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.90  = { by axiom 2 (condensed_detachment) R->L }
% 21.11/3.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(T, equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), T))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(T, equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), T)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.91  = { by axiom 3 (yql) }
% 21.11/3.92    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(T, equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), T))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.92  = { by axiom 1 (ifeq_axiom) }
% 21.11/3.93    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(T, equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), T))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.93  = { by axiom 1 (ifeq_axiom) R->L }
% 21.11/3.94    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(T, equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), T))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.94  = { by axiom 3 (yql) R->L }
% 21.11/3.95    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(T, equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), T)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(T, equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), T))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.95  = { by axiom 1 (ifeq_axiom) R->L }
% 21.11/3.96    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(T, equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), T)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(T, equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), T))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.96  = { by axiom 3 (yql) R->L }
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x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(T, equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), T)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(T, equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), T))), equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.97  = { by axiom 2 (condensed_detachment) }
% 21.11/3.97    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.97  = { by axiom 1 (ifeq_axiom) }
% 21.11/3.97    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.98  = { by axiom 2 (condensed_detachment) }
% 21.11/3.98    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.98  = { by axiom 1 (ifeq_axiom) }
% 21.11/3.98    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.98  = { by axiom 2 (condensed_detachment) }
% 21.11/3.98    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.98  = { by axiom 1 (ifeq_axiom) }
% 21.11/3.98    ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true)
% 21.11/3.98  = { by axiom 1 (ifeq_axiom) R->L }
% 21.11/3.98    ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/3.98  = { by axiom 2 (condensed_detachment) R->L }
% 21.11/3.98    ifeq(ifeq(is_a_theorem(equivalent(equivalent(x, x), equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, ifeq(is_a_theorem(equivalent(x, x)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/3.98  = { by axiom 3 (yql) }
% 21.11/3.98    ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(x, x)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/3.98  = { by axiom 1 (ifeq_axiom) }
% 21.11/3.98    ifeq(ifeq(is_a_theorem(equivalent(x, x)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/3.98  = { by axiom 1 (ifeq_axiom) R->L }
% 21.11/3.98    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/3.98  = { by axiom 2 (condensed_detachment) R->L }
% 21.11/3.98    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true, ifeq(is_a_theorem(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/3.98  = { by axiom 3 (yql) }
% 21.11/3.98    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/3.99  = { by axiom 1 (ifeq_axiom) }
% 21.11/3.99    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/3.99  = { by axiom 1 (ifeq_axiom) R->L }
% 21.11/3.99    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/3.99  = { by axiom 2 (condensed_detachment) R->L }
% 21.11/3.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(S, equivalent(x, x)), equivalent(equivalent(x, x), S))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(S, equivalent(x, x)), equivalent(equivalent(x, x), S)))), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/3.99  = { by axiom 3 (yql) }
% 21.11/3.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(S, equivalent(x, x)), equivalent(equivalent(x, x), S))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/3.99  = { by axiom 1 (ifeq_axiom) }
% 21.11/3.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(S, equivalent(x, x)), equivalent(equivalent(x, x), S))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x))))), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/4.00  = { by axiom 1 (ifeq_axiom) R->L }
% 21.11/4.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(S, equivalent(x, x)), equivalent(equivalent(x, x), S))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/4.00  = { by axiom 3 (yql) R->L }
% 21.11/4.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(S, equivalent(x, x)), equivalent(equivalent(x, x), S)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(S, equivalent(x, x)), equivalent(equivalent(x, x), S))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.11/4.00  = { by axiom 1 (ifeq_axiom) R->L }
% 21.71/4.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(S, equivalent(x, x)), equivalent(equivalent(x, x), S)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(S, equivalent(x, x)), equivalent(equivalent(x, x), S))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.00  = { by axiom 3 (yql) R->L }
% 21.71/4.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(S, equivalent(x, x)), equivalent(equivalent(x, x), S))), equivalent(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(S, equivalent(x, x)), equivalent(equivalent(x, x), S))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(S, equivalent(x, x)), equivalent(equivalent(x, x), S)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(S, equivalent(x, x)), equivalent(equivalent(x, x), S))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.00  = { by axiom 2 (condensed_detachment) }
% 21.71/4.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.01  = { by axiom 1 (ifeq_axiom) }
% 21.71/4.01    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.01  = { by axiom 1 (ifeq_axiom) R->L }
% 21.71/4.01    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.01  = { by axiom 3 (yql) R->L }
% 21.71/4.01    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(equivalent(x, x), equivalent(x, x)))), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(x, x), equivalent(x, x))), equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.01  = { by axiom 2 (condensed_detachment) }
% 21.71/4.01    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.01  = { by axiom 1 (ifeq_axiom) }
% 21.71/4.01    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true, is_a_theorem(equivalent(x, x)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.01  = { by axiom 1 (ifeq_axiom) R->L }
% 21.71/4.01    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true, ifeq(true, true, is_a_theorem(equivalent(x, x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.01  = { by axiom 2 (condensed_detachment) R->L }
% 21.71/4.01    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(X2, x), equivalent(x, X2))), equivalent(equivalent(x, x), equivalent(x, x)))), true, ifeq(is_a_theorem(equivalent(equivalent(x, x), equivalent(equivalent(X2, x), equivalent(x, X2)))), true, is_a_theorem(equivalent(equivalent(x, x), equivalent(x, x))), true), true), true, is_a_theorem(equivalent(x, x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.01  = { by axiom 3 (yql) }
% 21.71/4.02    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(X2, x), equivalent(x, X2))), equivalent(equivalent(x, x), equivalent(x, x)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(x, x), equivalent(x, x))), true), true), true, is_a_theorem(equivalent(x, x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.02  = { by axiom 1 (ifeq_axiom) }
% 21.71/4.02    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(X2, x), equivalent(x, X2))), equivalent(equivalent(x, x), equivalent(x, x)))), true, is_a_theorem(equivalent(equivalent(x, x), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.02  = { by axiom 1 (ifeq_axiom) R->L }
% 21.71/4.02    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(X2, x), equivalent(x, X2))), equivalent(equivalent(x, x), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(x, x), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.02  = { by axiom 3 (yql) R->L }
% 21.71/4.02    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(x, x), equivalent(equivalent(X2, x), equivalent(x, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(X2, x), equivalent(x, X2))), equivalent(equivalent(x, x), equivalent(x, x)))), true), true, is_a_theorem(equivalent(equivalent(x, x), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.02  = { by axiom 1 (ifeq_axiom) R->L }
% 21.71/4.02    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(x, x), equivalent(equivalent(X2, x), equivalent(x, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(X2, x), equivalent(x, X2))), equivalent(equivalent(x, x), equivalent(x, x)))), true), true), true, is_a_theorem(equivalent(equivalent(x, x), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.02  = { by axiom 3 (yql) R->L }
% 21.71/4.02    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(X2, x), equivalent(x, X2))), equivalent(equivalent(equivalent(x, x), equivalent(equivalent(X2, x), equivalent(x, X2))), equivalent(equivalent(x, x), equivalent(x, x))))), true, ifeq(is_a_theorem(equivalent(equivalent(x, x), equivalent(equivalent(X2, x), equivalent(x, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(equivalent(X2, x), equivalent(x, X2))), equivalent(equivalent(x, x), equivalent(x, x)))), true), true), true, is_a_theorem(equivalent(equivalent(x, x), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.02  = { by axiom 2 (condensed_detachment) }
% 21.71/4.02    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(x, x), equivalent(x, x))), true), true, is_a_theorem(equivalent(x, x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.02  = { by axiom 1 (ifeq_axiom) }
% 21.71/4.02    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(x, x), equivalent(x, x)), equivalent(x, x))), true, ifeq(is_a_theorem(equivalent(equivalent(x, x), equivalent(x, x))), true, is_a_theorem(equivalent(x, x)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.02  = { by axiom 2 (condensed_detachment) }
% 21.71/4.02    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.02  = { by axiom 1 (ifeq_axiom) }
% 21.71/4.02    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), x)), true, is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true), true)
% 21.71/4.02  = { by axiom 2 (condensed_detachment) }
% 21.71/4.02    true
% 21.71/4.02  % SZS output end Proof
% 21.71/4.02  
% 21.71/4.02  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------