Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n003.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 11:48:49 AM UTC 2026

% Result   : Unsatisfiable 4.95s 1.08s
% Output   : Proof 6.80s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37  % Computer : n003.cluster.edu
% 0.11/0.37  % Model    : x86_64 x86_64
% 0.11/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37  % Memory   : 8046.5625MB
% 0.11/0.37  % OS       : Linux 6.8.0-71-generic
% 0.11/0.37  % CPULimit : 300
% 0.11/0.37  % WCLimit  : 300
% 0.11/0.37  % DateTime : Sun Sep 27 15:18:40 UTC 2026
% 0.11/0.38  % CPUTime  : 
% 0.11/0.38  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.95/1.08  Command-line arguments: --flatten-regeneralise
% 4.95/1.08  
% 4.95/1.08  % SZS status Unsatisfiable
% 4.95/1.08  
% 5.98/1.26  % SZS output start Proof
% 5.98/1.26  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 5.98/1.26  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.
% 5.98/1.26  Axiom 3 (yql): is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, Y), equivalent(X, Z)))) = true.
% 5.98/1.26  
% 5.98/1.26  Goal 1 (prove_ec_5): is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))) = true.
% 5.98/1.26  Proof:
% 5.98/1.26    is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))
% 5.98/1.26  = { by axiom 1 (ifeq_axiom) R->L }
% 5.98/1.27    ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true)
% 5.98/1.27  = { by axiom 1 (ifeq_axiom) R->L }
% 5.98/1.27    ifeq(true, true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.27  = { by axiom 2 (condensed_detachment) R->L }
% 5.98/1.27    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.27  = { by axiom 1 (ifeq_axiom) R->L }
% 5.98/1.27    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.27  = { by axiom 2 (condensed_detachment) R->L }
% 5.98/1.28    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.28  = { by axiom 1 (ifeq_axiom) R->L }
% 5.98/1.28    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.28  = { by axiom 3 (yql) R->L }
% 5.98/1.28    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.28  = { by axiom 1 (ifeq_axiom) R->L }
% 5.98/1.29    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.29  = { by axiom 3 (yql) R->L }
% 5.98/1.29    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X))), equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.29  = { by axiom 2 (condensed_detachment) }
% 5.98/1.29    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.29  = { by axiom 1 (ifeq_axiom) }
% 5.98/1.29    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(X, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), X)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.29  = { by axiom 3 (yql) }
% 5.98/1.29    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.30  = { by axiom 1 (ifeq_axiom) }
% 5.98/1.30    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.30  = { by axiom 1 (ifeq_axiom) R->L }
% 5.98/1.30    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.30  = { by axiom 3 (yql) R->L }
% 5.98/1.30    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.30  = { by axiom 2 (condensed_detachment) }
% 5.98/1.30    ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 5.98/1.30  = { by axiom 1 (ifeq_axiom) }
% 5.98/1.30    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.30  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.30    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.30  = { by axiom 2 (condensed_detachment) R->L }
% 6.80/1.30    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))))), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.31  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.31    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.31  = { by axiom 2 (condensed_detachment) R->L }
% 6.80/1.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.31  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.31  = { by axiom 3 (yql) R->L }
% 6.80/1.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.32  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.32  = { by axiom 3 (yql) R->L }
% 6.80/1.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.32  = { by axiom 2 (condensed_detachment) }
% 6.80/1.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.32  = { by axiom 1 (ifeq_axiom) }
% 6.80/1.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.32  = { by axiom 3 (yql) }
% 6.80/1.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.33  = { by axiom 1 (ifeq_axiom) }
% 6.80/1.33    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.33  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.33    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.33  = { by axiom 3 (yql) R->L }
% 6.80/1.33    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.33  = { by axiom 2 (condensed_detachment) }
% 6.80/1.33    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.33  = { by axiom 1 (ifeq_axiom) }
% 6.80/1.33    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.33  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.34    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.34  = { by axiom 2 (condensed_detachment) R->L }
% 6.80/1.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z))), equivalent(equivalent(b, c), equivalent(b, c)))), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.34  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z))), equivalent(equivalent(b, c), equivalent(b, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.34  = { by axiom 3 (yql) R->L }
% 6.80/1.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z))), equivalent(equivalent(b, c), equivalent(b, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.34  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z))), equivalent(equivalent(b, c), equivalent(b, c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.34  = { by axiom 3 (yql) R->L }
% 6.80/1.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z))), equivalent(equivalent(b, c), equivalent(b, c))))), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z))), equivalent(equivalent(b, c), equivalent(b, c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.34  = { by axiom 2 (condensed_detachment) }
% 6.80/1.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.35  = { by axiom 1 (ifeq_axiom) }
% 6.80/1.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(Z, c), equivalent(b, Z)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.35  = { by axiom 3 (yql) }
% 6.80/1.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.35  = { by axiom 1 (ifeq_axiom) }
% 6.80/1.35    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.35  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.35    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.35  = { by axiom 3 (yql) R->L }
% 6.80/1.35    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)))), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.35  = { by axiom 2 (condensed_detachment) }
% 6.80/1.35    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.35  = { by axiom 1 (ifeq_axiom) }
% 6.80/1.35    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.35  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.35    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.35  = { by axiom 3 (yql) R->L }
% 6.80/1.35    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(a, equivalent(b, c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.35  = { by axiom 2 (condensed_detachment) }
% 6.80/1.36    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.36  = { by axiom 1 (ifeq_axiom) }
% 6.80/1.36    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.36  = { by axiom 2 (condensed_detachment) R->L }
% 6.80/1.36    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.36  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.36    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.36  = { by axiom 3 (yql) R->L }
% 6.80/1.36    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.36  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.36    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.36  = { by axiom 3 (yql) R->L }
% 6.80/1.36    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.36  = { by axiom 2 (condensed_detachment) }
% 6.80/1.36    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.37  = { by axiom 1 (ifeq_axiom) }
% 6.80/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.37  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.37  = { by axiom 2 (condensed_detachment) R->L }
% 6.80/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))))), true, ifeq(is_a_theorem(equivalent(equivalent(a, c), equivalent(equivalent(b, c), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.37  = { by axiom 3 (yql) }
% 6.80/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(a, c), equivalent(equivalent(b, c), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.37  = { by axiom 1 (ifeq_axiom) }
% 6.80/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(a, c), equivalent(equivalent(b, c), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.37  = { by axiom 3 (yql) }
% 6.80/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.37  = { by axiom 1 (ifeq_axiom) }
% 6.80/1.37    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.38  = { by axiom 1 (ifeq_axiom) R->L }
% 6.80/1.38    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.38  = { by axiom 2 (condensed_detachment) R->L }
% 6.80/1.38    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.38  = { by axiom 3 (yql) }
% 6.80/1.38    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.38  = { by axiom 1 (ifeq_axiom) }
% 6.80/1.38    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.38  = { by axiom 3 (yql) }
% 6.80/1.38    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.38  = { by axiom 1 (ifeq_axiom) }
% 6.80/1.39    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.39  = { by axiom 2 (condensed_detachment) }
% 6.80/1.39    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.39  = { by axiom 1 (ifeq_axiom) }
% 6.80/1.39    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true), true)
% 6.80/1.39  = { by axiom 2 (condensed_detachment) }
% 6.80/1.39    true
% 6.80/1.39  % SZS output end Proof
% 6.80/1.39  
% 6.80/1.39  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------