Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL011-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n004.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 11:48:50 AM UTC 2026

% Result   : Unsatisfiable 2.79s 0.84s
% Output   : Proof 4.72s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38  % Computer : n004.cluster.edu
% 0.11/0.38  % Model    : x86_64 x86_64
% 0.11/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38  % Memory   : 8046.5625MB
% 0.11/0.38  % OS       : Linux 6.8.0-71-generic
% 0.11/0.38  % CPULimit : 300
% 0.11/0.38  % WCLimit  : 300
% 0.11/0.38  % DateTime : Sun Sep 27 15:17:07 UTC 2026
% 0.11/0.38  % CPUTime  : 
% 0.11/0.38  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.79/0.84  Command-line arguments: --no-flatten-goal
% 2.79/0.84  
% 2.79/0.84  % SZS status Unsatisfiable
% 2.79/0.84  
% 3.60/1.00  % SZS output start Proof
% 3.60/1.00  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 3.60/1.00  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.
% 3.60/1.01  Axiom 3 (yqj): is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Y, Z)))) = true.
% 3.60/1.01  
% 3.60/1.01  Goal 1 (prove_yqf): is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))) = true.
% 3.60/1.01  Proof:
% 3.60/1.01    is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))
% 3.60/1.01  = { by axiom 1 (ifeq_axiom) R->L }
% 3.60/1.01    ifeq(true, true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.01  = { by axiom 2 (condensed_detachment) R->L }
% 3.60/1.01    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.01  = { by axiom 3 (yqj) }
% 3.60/1.01    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.01  = { by axiom 1 (ifeq_axiom) }
% 3.60/1.01    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.01  = { by axiom 1 (ifeq_axiom) R->L }
% 3.60/1.01    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.01  = { by axiom 2 (condensed_detachment) R->L }
% 3.60/1.01    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b))))), true, ifeq(is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.02  = { by axiom 3 (yqj) }
% 3.60/1.02    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.02  = { by axiom 1 (ifeq_axiom) }
% 3.60/1.02    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.02  = { by axiom 1 (ifeq_axiom) R->L }
% 3.60/1.02    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.02  = { by axiom 2 (condensed_detachment) R->L }
% 3.60/1.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.02  = { by axiom 3 (yqj) }
% 3.60/1.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.02  = { by axiom 1 (ifeq_axiom) }
% 3.60/1.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.02  = { by axiom 3 (yqj) }
% 3.60/1.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.02  = { by axiom 1 (ifeq_axiom) }
% 3.60/1.02    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.02  = { by axiom 1 (ifeq_axiom) R->L }
% 3.60/1.02    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.03  = { by axiom 2 (condensed_detachment) R->L }
% 3.60/1.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.03  = { by axiom 1 (ifeq_axiom) R->L }
% 3.60/1.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.03  = { by axiom 3 (yqj) R->L }
% 3.60/1.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.04  = { by axiom 1 (ifeq_axiom) R->L }
% 3.60/1.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.04  = { by axiom 3 (yqj) R->L }
% 3.60/1.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.04  = { by axiom 2 (condensed_detachment) }
% 3.60/1.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 3.60/1.04  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.05  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.05  = { by axiom 2 (condensed_detachment) R->L }
% 4.72/1.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.05  = { by axiom 3 (yqj) }
% 4.72/1.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.05  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.05  = { by axiom 3 (yqj) }
% 4.72/1.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.06  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.06  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.07  = { by axiom 2 (condensed_detachment) R->L }
% 4.72/1.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.07  = { by axiom 3 (yqj) }
% 4.72/1.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.07  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.08  = { by axiom 1 (ifeq_axiom) R->L }
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% 4.72/1.09  = { by axiom 3 (yqj) R->L }
% 4.72/1.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), 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% 4.72/1.09  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), 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equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.09  = { by axiom 3 (yqj) R->L }
% 4.72/1.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.10  = { by axiom 2 (condensed_detachment) }
% 4.72/1.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.10  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), Y))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.10  = { by axiom 2 (condensed_detachment) }
% 4.72/1.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.10  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.10    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X)), equivalent(equivalent(a, c), equivalent(a, c)))), true, ifeq(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))), X))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.10  = { by axiom 2 (condensed_detachment) }
% 4.72/1.10    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.10  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.10    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.10  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.10    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.10  = { by axiom 3 (yqj) R->L }
% 4.72/1.10    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(c, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.10  = { by axiom 2 (condensed_detachment) }
% 4.72/1.10    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.10  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.10    ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true)
% 4.72/1.10  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.10    ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.10  = { by axiom 2 (condensed_detachment) R->L }
% 4.72/1.10    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))))), true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.10  = { by axiom 3 (yqj) }
% 4.72/1.10    ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.10  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.10    ifeq(ifeq(is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.11  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.11    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.11  = { by axiom 2 (condensed_detachment) R->L }
% 4.72/1.11    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.11  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.11    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.11  = { by axiom 2 (condensed_detachment) R->L }
% 4.72/1.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))))), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.11  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.11  = { by axiom 2 (condensed_detachment) R->L }
% 4.72/1.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))))), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))))), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.11  = { by axiom 3 (yqj) }
% 4.72/1.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))))), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.12  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))))), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.12  = { by axiom 3 (yqj) }
% 4.72/1.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))))), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.12  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))))), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.12  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))))), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.12  = { by axiom 3 (yqj) R->L }
% 4.72/1.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))))), equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.13  = { by axiom 2 (condensed_detachment) }
% 4.72/1.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.13  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.13  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.13  = { by axiom 3 (yqj) R->L }
% 4.72/1.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.13  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true), true), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.13  = { by axiom 3 (yqj) R->L }
% 4.72/1.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))))), true, is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(equivalent(a, a), equivalent(a, a)), equivalent(a, a))), equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(a, a), equivalent(a, a))), W))), true), true), true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.13  = { by axiom 2 (condensed_detachment) }
% 4.72/1.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.13  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.13    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.13  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.13    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.13  = { by axiom 2 (condensed_detachment) R->L }
% 4.72/1.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.13  = { by axiom 3 (yqj) }
% 4.72/1.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 3 (yqj) }
% 4.72/1.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.14    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a)))), true, ifeq(is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)), equivalent(a, a))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 2 (condensed_detachment) }
% 4.72/1.14    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.14    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true, is_a_theorem(equivalent(a, a)), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.14    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true), true, is_a_theorem(equivalent(a, a)), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 3 (yqj) R->L }
% 4.72/1.14    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), true, is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true), true, is_a_theorem(equivalent(a, a)), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.14    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), true, is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true), true), true, is_a_theorem(equivalent(a, a)), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 3 (yqj) R->L }
% 4.72/1.14    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a))), equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z)))), true, ifeq(is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(a, a), equivalent(a, a)))), true, is_a_theorem(equivalent(equivalent(Z, equivalent(a, a)), equivalent(equivalent(equivalent(a, a), equivalent(a, a)), Z))), true), true), true, is_a_theorem(equivalent(a, a)), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 2 (condensed_detachment) }
% 4.72/1.14    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(a, a)), true), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.14    ifeq(ifeq(ifeq(is_a_theorem(equivalent(a, a)), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 1 (ifeq_axiom) R->L }
% 4.72/1.14    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(a, a)), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 3 (yqj) R->L }
% 4.72/1.14    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(a, a), equivalent(equivalent(b, a), equivalent(a, b)))), true, ifeq(is_a_theorem(equivalent(a, a)), true, is_a_theorem(equivalent(equivalent(b, a), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 2 (condensed_detachment) }
% 4.72/1.14    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 1 (ifeq_axiom) }
% 4.72/1.14    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a)), equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true), true)
% 4.72/1.14  = { by axiom 2 (condensed_detachment) }
% 4.72/1.14    true
% 4.72/1.14  % SZS output end Proof
% 4.72/1.14  
% 4.72/1.14  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------