Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL131-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:49:07 AM UTC 2026

% Result   : Unsatisfiable 3.56s 0.94s
% Output   : Proof 72.69s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL131-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37  % Computer : n009.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 15:23:15 UTC 2026
% 0.11/0.37  % CPUTime  : 
% 0.11/0.38  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.56/0.94  Command-line arguments: --no-flatten-goal
% 3.56/0.94  
% 3.56/0.94  % SZS status Unsatisfiable
% 3.56/0.94  
% 40.94/6.39  % SZS output start Proof
% 40.94/6.39  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 40.94/6.39  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.
% 41.64/6.49  Axiom 3 (s_6): is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X)) = true.
% 41.64/6.49  
% 41.64/6.49  Goal 1 (prove_lg_2): is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))) = true.
% 41.64/6.49  Proof:
% 41.64/6.49    is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 41.64/6.49  = { by axiom 1 (ifeq_axiom) R->L }
% 41.64/6.49    ifeq(true, true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 41.64/6.50  = { by axiom 2 (condensed_detachment) R->L }
% 41.64/6.50    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 42.33/6.50  = { by axiom 1 (ifeq_axiom) R->L }
% 42.33/6.50    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 42.33/6.50  = { by axiom 2 (condensed_detachment) R->L }
% 42.33/6.51    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 42.33/6.52  = { by axiom 3 (s_6) }
% 42.33/6.53    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 42.33/6.54  = { by axiom 1 (ifeq_axiom) }
% 42.33/6.55    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 42.33/6.55  = { by axiom 1 (ifeq_axiom) R->L }
% 42.33/6.56    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, 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% 42.33/6.57  = { by axiom 2 (condensed_detachment) R->L }
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% 42.33/6.59  = { by axiom 3 (s_6) }
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% 43.04/6.61  = { by axiom 1 (ifeq_axiom) }
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% 43.04/6.62  = { by axiom 3 (s_6) }
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% 43.04/6.63  = { by axiom 1 (ifeq_axiom) }
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% 43.04/6.64  = { by axiom 1 (ifeq_axiom) R->L }
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% 43.04/6.65  = { by axiom 3 (s_6) R->L }
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% 43.04/6.66  = { by axiom 2 (condensed_detachment) }
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% 43.04/6.67  = { by axiom 1 (ifeq_axiom) }
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% 43.04/6.68  = { by axiom 1 (ifeq_axiom) R->L }
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% 43.76/6.70  = { by axiom 2 (condensed_detachment) R->L }
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% 43.76/6.71  = { by axiom 1 (ifeq_axiom) R->L }
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% 43.76/6.73  = { by axiom 2 (condensed_detachment) R->L }
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% 44.46/6.80  = { by axiom 3 (s_6) }
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% 44.46/6.82  = { by axiom 1 (ifeq_axiom) R->L }
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% 44.46/6.84  = { by axiom 3 (s_6) R->L }
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% 44.46/6.85  = { by axiom 2 (condensed_detachment) }
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% 44.46/6.87  = { by axiom 1 (ifeq_axiom) }
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% 44.46/6.89  = { by axiom 1 (ifeq_axiom) R->L }
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% 45.17/6.93  = { by axiom 2 (condensed_detachment) R->L }
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% 45.17/6.96  = { by axiom 1 (ifeq_axiom) R->L }
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% 46.08/7.04  = { by axiom 3 (s_6) }
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% 46.08/7.08  = { by axiom 1 (ifeq_axiom) }
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% 46.08/7.12  = { by axiom 3 (s_6) }
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% 46.80/7.15  = { by axiom 1 (ifeq_axiom) }
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% 46.80/7.19  = { by axiom 3 (s_6) R->L }
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% 47.27/7.23  = { by axiom 1 (ifeq_axiom) }
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% 47.27/7.25  = { by axiom 1 (ifeq_axiom) R->L }
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% 47.27/7.27  = { by axiom 3 (s_6) R->L }
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% 47.27/7.28  = { by axiom 1 (ifeq_axiom) R->L }
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% 47.27/7.30  = { by axiom 3 (s_6) R->L }
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% 47.97/7.32  = { by axiom 2 (condensed_detachment) }
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% 47.97/7.33  = { by axiom 1 (ifeq_axiom) }
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% 47.97/7.35  = { by axiom 1 (ifeq_axiom) R->L }
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% 47.97/7.36  = { by axiom 2 (condensed_detachment) R->L }
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% 47.97/7.38  = { by axiom 3 (s_6) }
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% 48.68/7.40  = { by axiom 1 (ifeq_axiom) }
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% 48.68/7.43  = { by axiom 1 (ifeq_axiom) R->L }
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% 48.68/7.45  = { by axiom 3 (s_6) R->L }
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% 48.68/7.47  = { by axiom 1 (ifeq_axiom) R->L }
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% 48.68/7.49  = { by axiom 3 (s_6) R->L }
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% 49.38/7.52  = { by axiom 2 (condensed_detachment) }
% 49.38/7.53    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), 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% 49.38/7.53  = { by axiom 1 (ifeq_axiom) }
% 49.38/7.53    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), 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% 49.38/7.53  = { by axiom 2 (condensed_detachment) }
% 49.38/7.54    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 49.38/7.54  = { by axiom 1 (ifeq_axiom) }
% 49.38/7.54    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 49.38/7.54  = { by axiom 2 (condensed_detachment) }
% 49.38/7.54    ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 49.38/7.54  = { by axiom 1 (ifeq_axiom) }
% 49.38/7.54    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 49.38/7.55  = { by axiom 1 (ifeq_axiom) R->L }
% 49.38/7.55    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 49.38/7.56  = { by axiom 2 (condensed_detachment) R->L }
% 49.38/7.56    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 49.38/7.56  = { by axiom 1 (ifeq_axiom) R->L }
% 49.38/7.57    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 49.38/7.57  = { by axiom 2 (condensed_detachment) R->L }
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e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), 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% 50.10/7.60  = { by axiom 3 (s_6) }
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% 50.10/7.64  = { by axiom 1 (ifeq_axiom) }
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% 51.50/7.83  = { by axiom 3 (s_6) R->L }
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% 51.50/7.85  = { by axiom 2 (condensed_detachment) }
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% 51.50/7.86  = { by axiom 1 (ifeq_axiom) }
% 51.50/7.86    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 51.50/7.86  = { by axiom 1 (ifeq_axiom) R->L }
% 51.50/7.86    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 51.50/7.86  = { by axiom 3 (s_6) R->L }
% 51.50/7.87    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), 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% 51.50/7.87  = { by axiom 2 (condensed_detachment) }
% 51.50/7.87    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 51.50/7.88  = { by axiom 1 (ifeq_axiom) }
% 51.50/7.88    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 51.50/7.89  = { by axiom 1 (ifeq_axiom) R->L }
% 51.50/7.89    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 51.50/7.89  = { by axiom 2 (condensed_detachment) R->L }
% 52.22/7.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), 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% 52.22/7.91  = { by axiom 3 (s_6) }
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% 52.22/7.94  = { by axiom 1 (ifeq_axiom) }
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% 52.22/7.96  = { by axiom 1 (ifeq_axiom) R->L }
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% 52.22/7.98  = { by axiom 2 (condensed_detachment) R->L }
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% 53.14/8.04  = { by axiom 1 (ifeq_axiom) }
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% 53.14/8.08  = { by axiom 3 (s_6) }
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% 53.85/8.14  = { by axiom 1 (ifeq_axiom) }
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% 53.85/8.17  = { by axiom 1 (ifeq_axiom) R->L }
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% 55.74/8.49  = { by axiom 1 (ifeq_axiom) R->L }
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% 56.45/8.59  = { by axiom 3 (s_6) R->L }
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% 58.58/8.80  = { by axiom 2 (condensed_detachment) }
% 58.58/8.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 58.58/8.81  = { by axiom 1 (ifeq_axiom) }
% 58.58/8.81    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 58.58/8.81  = { by axiom 1 (ifeq_axiom) R->L }
% 58.58/8.82    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 58.58/8.82  = { by axiom 2 (condensed_detachment) R->L }
% 58.58/8.83    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), 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equivalent(equivalent(equivalent(V3, U3), equivalent(T3, U3)), equivalent(V3, T3)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 58.58/8.83  = { by axiom 3 (s_6) }
% 58.58/8.83    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(V3, U3), equivalent(T3, U3)), equivalent(V3, T3)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 58.58/8.84  = { by axiom 1 (ifeq_axiom) }
% 58.58/8.84    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(V3, U3), equivalent(T3, U3)), equivalent(V3, T3)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 58.58/8.85  = { by axiom 1 (ifeq_axiom) R->L }
% 58.58/8.85    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(V3, U3), equivalent(T3, U3)), equivalent(V3, T3)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 58.58/8.86  = { by axiom 3 (s_6) R->L }
% 58.58/8.87    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), 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% 58.58/8.87  = { by axiom 1 (ifeq_axiom) R->L }
% 58.58/8.88    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), 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% 58.58/8.88  = { by axiom 3 (s_6) R->L }
% 58.58/8.89    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), 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equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), 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equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 58.58/8.89  = { by axiom 2 (condensed_detachment) }
% 58.58/8.89    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 58.58/8.89  = { by axiom 1 (ifeq_axiom) }
% 58.58/8.89    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 58.58/8.89  = { by axiom 2 (condensed_detachment) }
% 58.58/8.89    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 58.58/8.90  = { by axiom 1 (ifeq_axiom) }
% 58.58/8.90    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 59.29/8.90  = { by axiom 1 (ifeq_axiom) R->L }
% 59.29/8.90    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 59.29/8.91  = { by axiom 2 (condensed_detachment) R->L }
% 59.29/8.91    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 59.29/8.92  = { by axiom 1 (ifeq_axiom) R->L }
% 59.29/8.92    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 59.29/8.94  = { by axiom 2 (condensed_detachment) R->L }
% 59.29/8.94    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, 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% 59.29/8.95  = { by axiom 1 (ifeq_axiom) R->L }
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% 59.29/8.97  = { by axiom 2 (condensed_detachment) R->L }
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% 59.29/9.00  = { by axiom 3 (s_6) }
% 59.29/9.01    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, 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% 60.21/9.03  = { by axiom 1 (ifeq_axiom) }
% 60.21/9.04    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, 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% 60.21/9.06  = { by axiom 1 (ifeq_axiom) R->L }
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% 60.21/9.10  = { by axiom 3 (s_6) R->L }
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% 60.21/9.12  = { by axiom 1 (ifeq_axiom) R->L }
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% 60.91/9.19  = { by axiom 2 (condensed_detachment) }
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% 61.40/9.21  = { by axiom 1 (ifeq_axiom) }
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% 61.40/9.22  = { by axiom 1 (ifeq_axiom) R->L }
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% 61.40/9.23  = { by axiom 3 (s_6) R->L }
% 61.40/9.24    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, 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% 61.40/9.25  = { by axiom 2 (condensed_detachment) }
% 61.40/9.25    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(S3, equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(S3, equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(S3, equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(S3, equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 61.40/9.27  = { by axiom 1 (ifeq_axiom) }
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% 61.40/9.28  = { by axiom 1 (ifeq_axiom) R->L }
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% 61.40/9.29  = { by axiom 2 (condensed_detachment) R->L }
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equivalent(S3, equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, 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% 62.11/9.34  = { by axiom 3 (s_6) }
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% 62.11/9.39  = { by axiom 1 (ifeq_axiom) }
% 62.81/9.40    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, 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% 62.81/9.43  = { by axiom 1 (ifeq_axiom) R->L }
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% 64.22/9.62  = { by axiom 1 (ifeq_axiom) }
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% 64.22/9.64  = { by axiom 1 (ifeq_axiom) R->L }
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% 64.22/9.67  = { by axiom 3 (s_6) R->L }
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% 64.22/9.69  = { by axiom 2 (condensed_detachment) }
% 64.92/9.70    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, 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% 64.92/9.71  = { by axiom 1 (ifeq_axiom) }
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% 64.92/9.72  = { by axiom 1 (ifeq_axiom) R->L }
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% 64.92/9.72  = { by axiom 3 (s_6) R->L }
% 64.92/9.73    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, 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% 64.92/9.74  = { by axiom 2 (condensed_detachment) }
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% 64.92/9.74  = { by axiom 1 (ifeq_axiom) }
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% 64.92/9.75  = { by axiom 1 (ifeq_axiom) R->L }
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% 64.92/9.76  = { by axiom 2 (condensed_detachment) R->L }
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% 64.92/9.78  = { by axiom 3 (s_6) }
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% 64.92/9.79  = { by axiom 1 (ifeq_axiom) }
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% 65.62/9.80  = { by axiom 1 (ifeq_axiom) R->L }
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% 65.62/9.82  = { by axiom 3 (s_6) R->L }
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% 65.62/9.83  = { by axiom 1 (ifeq_axiom) R->L }
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% 65.62/9.84  = { by axiom 3 (s_6) R->L }
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% 65.62/9.86  = { by axiom 2 (condensed_detachment) }
% 65.62/9.86    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, 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% 65.62/9.86  = { by axiom 1 (ifeq_axiom) }
% 65.62/9.86    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, 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equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 65.62/9.87  = { by axiom 2 (condensed_detachment) }
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% 65.62/9.88  = { by axiom 1 (ifeq_axiom) }
% 65.62/9.88    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 65.62/9.89  = { by axiom 1 (ifeq_axiom) R->L }
% 65.62/9.89    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 66.32/9.90  = { by axiom 2 (condensed_detachment) R->L }
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% 66.32/9.93  = { by axiom 3 (s_6) }
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% 66.32/9.96  = { by axiom 1 (ifeq_axiom) }
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% 66.32/9.98  = { by axiom 1 (ifeq_axiom) R->L }
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% 66.32/10.01  = { by axiom 2 (condensed_detachment) R->L }
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% 67.23/10.06  = { by axiom 3 (s_6) }
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% 67.23/10.12  = { by axiom 1 (ifeq_axiom) }
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% 67.95/10.18  = { by axiom 1 (ifeq_axiom) R->L }
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% 68.44/10.26  = { by axiom 3 (s_6) R->L }
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% 69.88/10.43  = { by axiom 1 (ifeq_axiom) }
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% 69.88/10.45  = { by axiom 1 (ifeq_axiom) R->L }
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% 69.88/10.47  = { by axiom 3 (s_6) R->L }
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% 69.88/10.49  = { by axiom 2 (condensed_detachment) }
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% 70.58/10.50  = { by axiom 1 (ifeq_axiom) }
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% 70.58/10.52  = { by axiom 1 (ifeq_axiom) R->L }
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% 70.58/10.53  = { by axiom 2 (condensed_detachment) R->L }
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% 70.58/10.56  = { by axiom 3 (s_6) }
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% 71.28/10.61  = { by axiom 1 (ifeq_axiom) }
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% 71.28/10.64  = { by axiom 1 (ifeq_axiom) R->L }
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% 72.69/10.82  = { by axiom 1 (ifeq_axiom) }
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% 72.69/10.84  = { by axiom 1 (ifeq_axiom) R->L }
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true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), 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% 72.69/10.88  = { by axiom 2 (condensed_detachment) }
% 72.69/10.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), 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% 72.69/10.88  = { by axiom 1 (ifeq_axiom) }
% 72.69/10.89    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), 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true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 72.69/10.89  = { by axiom 2 (condensed_detachment) }
% 72.69/10.89    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 72.69/10.89  = { by axiom 1 (ifeq_axiom) }
% 72.69/10.89    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), a)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 72.69/10.89  = { by axiom 2 (condensed_detachment) }
% 72.69/10.89    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 72.69/10.89  = { by axiom 1 (ifeq_axiom) }
% 72.69/10.89    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 72.69/10.89  = { by axiom 1 (ifeq_axiom) R->L }
% 72.69/10.89    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(true, true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true)
% 72.69/10.89  = { by axiom 3 (s_6) R->L }
% 72.69/10.89    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true)
% 72.69/10.89  = { by axiom 2 (condensed_detachment) }
% 72.69/10.89    true
% 72.69/10.89  % SZS output end Proof
% 72.69/10.89  
% 72.69/10.89  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------