Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL022-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:48:50 AM UTC 2026

% Result   : Unsatisfiable 0.10s 0.45s
% Output   : Proof 2.77s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL022-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37  % Computer : n019.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Sun Sep 27 15:17:48 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.10/0.37  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45  Command-line arguments: --no-flatten-goal
% 0.10/0.45  
% 0.10/0.45  % SZS status Unsatisfiable
% 0.10/0.45  
% 2.06/0.72  % SZS output start Proof
% 2.06/0.72  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.06/0.72  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.
% 2.06/0.72  Axiom 3 (yql): is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, Y), equivalent(X, Z)))) = true.
% 2.06/0.72  
% 2.06/0.72  Goal 1 (prove_ec_1): is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))) = true.
% 2.06/0.72  Proof:
% 2.06/0.72    is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 2.06/0.73  = { by axiom 1 (ifeq_axiom) R->L }
% 2.06/0.73    ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.73  = { by axiom 2 (condensed_detachment) R->L }
% 2.06/0.73    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.73  = { by axiom 1 (ifeq_axiom) R->L }
% 2.06/0.73    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.74  = { by axiom 2 (condensed_detachment) R->L }
% 2.06/0.74    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.74  = { by axiom 1 (ifeq_axiom) R->L }
% 2.06/0.75    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.75  = { by axiom 2 (condensed_detachment) R->L }
% 2.06/0.75    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(X, equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), X))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(X, equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), X))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(X, equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(X, equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), X))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.75  = { by axiom 3 (yql) }
% 2.06/0.75    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(X, equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(X, equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), X))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.76  = { by axiom 1 (ifeq_axiom) }
% 2.06/0.76    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(X, equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(X, equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), X))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.76  = { by axiom 3 (yql) }
% 2.06/0.76    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(X, equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), X))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.76  = { by axiom 1 (ifeq_axiom) }
% 2.06/0.77    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(X, equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), X))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.77  = { by axiom 1 (ifeq_axiom) R->L }
% 2.06/0.77    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(X, equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), X))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.77  = { by axiom 3 (yql) R->L }
% 2.06/0.77    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(X, equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), X))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(X, equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.77  = { by axiom 2 (condensed_detachment) }
% 2.06/0.78    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.78  = { by axiom 1 (ifeq_axiom) }
% 2.06/0.78    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.78  = { by axiom 1 (ifeq_axiom) R->L }
% 2.06/0.78    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.79  = { by axiom 2 (condensed_detachment) R->L }
% 2.06/0.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.80  = { by axiom 3 (yql) }
% 2.06/0.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.06/0.80  = { by axiom 1 (ifeq_axiom) }
% 2.48/0.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.81  = { by axiom 1 (ifeq_axiom) R->L }
% 2.48/0.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.82  = { by axiom 2 (condensed_detachment) R->L }
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% 2.48/0.82  = { by axiom 3 (yql) }
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% 2.48/0.83  = { by axiom 1 (ifeq_axiom) }
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% 2.48/0.84  = { by axiom 3 (yql) }
% 2.48/0.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.85  = { by axiom 1 (ifeq_axiom) }
% 2.48/0.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.86  = { by axiom 1 (ifeq_axiom) R->L }
% 2.48/0.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.86  = { by axiom 3 (yql) R->L }
% 2.48/0.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(Y, equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), Y))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, 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% 2.48/0.87  = { by axiom 2 (condensed_detachment) }
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% 2.48/0.87  = { by axiom 1 (ifeq_axiom) }
% 2.48/0.87    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.87  = { by axiom 1 (ifeq_axiom) R->L }
% 2.48/0.87    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.87  = { by axiom 3 (yql) R->L }
% 2.48/0.88    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.88  = { by axiom 2 (condensed_detachment) }
% 2.48/0.88    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.88  = { by axiom 1 (ifeq_axiom) }
% 2.48/0.88    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.88  = { by axiom 1 (ifeq_axiom) R->L }
% 2.48/0.88    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.88  = { by axiom 3 (yql) R->L }
% 2.48/0.88    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.88  = { by axiom 2 (condensed_detachment) }
% 2.48/0.88    ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.88  = { by axiom 1 (ifeq_axiom) }
% 2.48/0.88    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.88  = { by axiom 1 (ifeq_axiom) R->L }
% 2.48/0.88    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.88  = { by axiom 2 (condensed_detachment) R->L }
% 2.48/0.88    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(equivalent(c, b), equivalent(b, c)))), true, ifeq(is_a_theorem(equivalent(b, b)), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.88  = { by axiom 3 (yql) }
% 2.48/0.88    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(b, b)), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.88  = { by axiom 1 (ifeq_axiom) }
% 2.48/0.88    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(b, b)), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.88  = { by axiom 1 (ifeq_axiom) R->L }
% 2.48/0.88    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.89  = { by axiom 2 (condensed_detachment) R->L }
% 2.48/0.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true, ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.89  = { by axiom 3 (yql) }
% 2.48/0.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.89  = { by axiom 1 (ifeq_axiom) }
% 2.48/0.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.89  = { by axiom 1 (ifeq_axiom) R->L }
% 2.48/0.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.89  = { by axiom 2 (condensed_detachment) R->L }
% 2.48/0.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Z, equivalent(b, b)), equivalent(equivalent(b, b), Z))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Z, equivalent(b, b)), equivalent(equivalent(b, b), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.89  = { by axiom 3 (yql) }
% 2.48/0.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Z, equivalent(b, b)), equivalent(equivalent(b, b), Z))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.89  = { by axiom 1 (ifeq_axiom) }
% 2.48/0.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Z, equivalent(b, b)), equivalent(equivalent(b, b), Z))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.90  = { by axiom 1 (ifeq_axiom) R->L }
% 2.48/0.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Z, equivalent(b, b)), equivalent(equivalent(b, b), Z))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.90  = { by axiom 3 (yql) R->L }
% 2.48/0.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Z, equivalent(b, b)), equivalent(equivalent(b, b), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Z, equivalent(b, b)), equivalent(equivalent(b, b), Z))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.90  = { by axiom 1 (ifeq_axiom) R->L }
% 2.48/0.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Z, equivalent(b, b)), equivalent(equivalent(b, b), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Z, equivalent(b, b)), equivalent(equivalent(b, b), Z))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.48/0.90  = { by axiom 3 (yql) R->L }
% 2.77/0.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Z, equivalent(b, b)), equivalent(equivalent(b, b), Z))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Z, equivalent(b, b)), equivalent(equivalent(b, b), Z))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Z, equivalent(b, b)), equivalent(equivalent(b, b), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(Z, equivalent(b, b)), equivalent(equivalent(b, b), Z))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.90  = { by axiom 2 (condensed_detachment) }
% 2.77/0.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.90  = { by axiom 1 (ifeq_axiom) }
% 2.77/0.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.91  = { by axiom 1 (ifeq_axiom) R->L }
% 2.77/0.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.91  = { by axiom 3 (yql) R->L }
% 2.77/0.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), equivalent(b, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.91  = { by axiom 2 (condensed_detachment) }
% 2.77/0.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.91  = { by axiom 1 (ifeq_axiom) }
% 2.77/0.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, is_a_theorem(equivalent(b, b)), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.91  = { by axiom 1 (ifeq_axiom) R->L }
% 2.77/0.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(true, true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.91  = { by axiom 2 (condensed_detachment) R->L }
% 2.77/0.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(W, b), equivalent(b, W))), equivalent(equivalent(b, b), equivalent(b, b)))), true, ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(equivalent(W, b), equivalent(b, W)))), true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.91  = { by axiom 3 (yql) }
% 2.77/0.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(W, b), equivalent(b, W))), equivalent(equivalent(b, b), equivalent(b, b)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.91  = { by axiom 1 (ifeq_axiom) }
% 2.77/0.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(W, b), equivalent(b, W))), equivalent(equivalent(b, b), equivalent(b, b)))), true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.91  = { by axiom 1 (ifeq_axiom) R->L }
% 2.77/0.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(W, b), equivalent(b, W))), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.91  = { by axiom 3 (yql) R->L }
% 2.77/0.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(equivalent(W, b), equivalent(b, W)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(W, b), equivalent(b, W))), equivalent(equivalent(b, b), equivalent(b, b)))), true), true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.92  = { by axiom 1 (ifeq_axiom) R->L }
% 2.77/0.92    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(equivalent(W, b), equivalent(b, W)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(W, b), equivalent(b, W))), equivalent(equivalent(b, b), equivalent(b, b)))), true), true), true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.92  = { by axiom 3 (yql) R->L }
% 2.77/0.92    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(W, b), equivalent(b, W))), equivalent(equivalent(equivalent(b, b), equivalent(equivalent(W, b), equivalent(b, W))), equivalent(equivalent(b, b), equivalent(b, b))))), true, ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(equivalent(W, b), equivalent(b, W)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(W, b), equivalent(b, W))), equivalent(equivalent(b, b), equivalent(b, b)))), true), true), true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.92  = { by axiom 2 (condensed_detachment) }
% 2.77/0.92    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.92  = { by axiom 1 (ifeq_axiom) }
% 2.77/0.92    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(b, b))), true, ifeq(is_a_theorem(equivalent(equivalent(b, b), equivalent(b, b))), true, is_a_theorem(equivalent(b, b)), true), true), true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.92  = { by axiom 2 (condensed_detachment) }
% 2.77/0.92    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.92  = { by axiom 1 (ifeq_axiom) }
% 2.77/0.92    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.92  = { by axiom 1 (ifeq_axiom) R->L }
% 2.77/0.92    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.92  = { by axiom 3 (yql) R->L }
% 2.77/0.92    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(b, c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))))), true, ifeq(is_a_theorem(equivalent(equivalent(c, b), equivalent(b, c))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)), equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.92  = { by axiom 2 (condensed_detachment) }
% 2.77/0.92    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.92  = { by axiom 1 (ifeq_axiom) }
% 2.77/0.92    ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 2.77/0.92  = { by axiom 1 (ifeq_axiom) R->L }
% 2.77/0.92    ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true), true)
% 2.77/0.92  = { by axiom 3 (yql) R->L }
% 2.77/0.92    ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true, ifeq(is_a_theorem(equivalent(equivalent(c, b), equivalent(equivalent(a, b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true), true)
% 2.77/0.92  = { by axiom 2 (condensed_detachment) }
% 2.77/0.92    true
% 2.77/0.92  % SZS output end Proof
% 2.77/0.92  
% 2.77/0.92  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------