Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL049-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:48:54 AM UTC 2026

% Result   : Unsatisfiable 29.20s 4.05s
% Output   : Proof 48.30s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01  % Problem  : LCL049-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.31  % Computer : n012.cluster.edu
% 0.02/0.31  % Model    : x86_64 x86_64
% 0.02/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.31  % Memory   : 8046.5625MB
% 0.02/0.31  % OS       : Linux 6.8.0-71-generic
% 0.02/0.31  % CPULimit : 300
% 0.02/0.31  % WCLimit  : 300
% 0.02/0.31  % DateTime : Sun Sep 27 15:18:34 UTC 2026
% 0.02/0.31  % CPUTime  : 
% 0.02/0.31  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.20/4.05  Command-line arguments: --no-flatten-goal
% 29.20/4.05  
% 29.20/4.05  % SZS status Unsatisfiable
% 29.20/4.05  
% 43.22/5.82  % SZS output start Proof
% 43.22/5.82  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 43.22/5.82  Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 43.22/5.82  Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 43.22/5.82  Axiom 4 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 43.22/5.86  Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 43.22/5.86  
% 43.22/5.86  Goal 1 (prove_cn_20): is_a_theorem(implies(a, implies(implies(a, b), b))) = true.
% 43.22/5.86  Proof:
% 43.22/5.86    is_a_theorem(implies(a, implies(implies(a, b), b)))
% 43.22/5.86  = { by axiom 1 (ifeq_axiom) R->L }
% 43.22/5.86    ifeq(true, true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.86  = { by axiom 4 (condensed_detachment) R->L }
% 43.22/5.86    ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.86  = { by axiom 1 (ifeq_axiom) R->L }
% 43.22/5.86    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.86  = { by axiom 4 (condensed_detachment) R->L }
% 43.22/5.86    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.86  = { by axiom 1 (ifeq_axiom) R->L }
% 43.22/5.86    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.86  = { by axiom 4 (condensed_detachment) R->L }
% 43.22/5.86    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.87  = { by axiom 2 (cn_3) }
% 43.22/5.87    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.87  = { by axiom 1 (ifeq_axiom) }
% 43.22/5.87    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.87  = { by axiom 5 (cn_1) }
% 43.22/5.87    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.87  = { by axiom 1 (ifeq_axiom) }
% 43.22/5.87    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.87  = { by axiom 1 (ifeq_axiom) R->L }
% 43.22/5.88    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.88  = { by axiom 3 (cn_2) R->L }
% 43.22/5.88    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.88  = { by axiom 4 (condensed_detachment) }
% 43.22/5.88    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.88  = { by axiom 1 (ifeq_axiom) }
% 43.22/5.88    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.88  = { by axiom 1 (ifeq_axiom) R->L }
% 43.22/5.88    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.88  = { by axiom 4 (condensed_detachment) R->L }
% 43.22/5.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.89  = { by axiom 5 (cn_1) }
% 43.22/5.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.89  = { by axiom 1 (ifeq_axiom) }
% 43.22/5.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.89  = { by axiom 1 (ifeq_axiom) R->L }
% 43.22/5.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.89  = { by axiom 4 (condensed_detachment) R->L }
% 43.22/5.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 43.22/5.90  = { by axiom 1 (ifeq_axiom) R->L }
% 43.22/5.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.90  = { by axiom 5 (cn_1) R->L }
% 44.04/5.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.90  = { by axiom 1 (ifeq_axiom) R->L }
% 44.04/5.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.91  = { by axiom 5 (cn_1) R->L }
% 44.04/5.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.91  = { by axiom 4 (condensed_detachment) }
% 44.04/5.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.92  = { by axiom 1 (ifeq_axiom) }
% 44.04/5.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.93  = { by axiom 1 (ifeq_axiom) R->L }
% 44.04/5.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.94  = { by axiom 4 (condensed_detachment) R->L }
% 44.04/5.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.95  = { by axiom 1 (ifeq_axiom) R->L }
% 44.04/5.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.95  = { by axiom 5 (cn_1) R->L }
% 44.04/5.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b)), implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.96  = { by axiom 1 (ifeq_axiom) R->L }
% 44.04/5.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b)), implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.97  = { by axiom 2 (cn_3) R->L }
% 44.04/5.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b)), implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.97  = { by axiom 4 (condensed_detachment) }
% 44.04/5.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.98  = { by axiom 1 (ifeq_axiom) }
% 44.04/5.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.99  = { by axiom 1 (ifeq_axiom) R->L }
% 44.04/5.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/5.99  = { by axiom 5 (cn_1) R->L }
% 44.04/5.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)))), true, is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/6.00  = { by axiom 1 (ifeq_axiom) R->L }
% 44.04/6.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)))), true, ifeq(true, true, is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/6.00  = { by axiom 3 (cn_2) R->L }
% 44.04/6.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), b), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/6.01  = { by axiom 4 (condensed_detachment) }
% 44.04/6.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/6.01  = { by axiom 1 (ifeq_axiom) }
% 44.04/6.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.04/6.02  = { by axiom 1 (ifeq_axiom) R->L }
% 44.04/6.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.02  = { by axiom 5 (cn_1) R->L }
% 44.92/6.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b)), implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))), b), implies(implies(a, b), b)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.03  = { by axiom 4 (condensed_detachment) }
% 44.92/6.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.03  = { by axiom 1 (ifeq_axiom) }
% 44.92/6.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.04  = { by axiom 1 (ifeq_axiom) R->L }
% 44.92/6.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.04  = { by axiom 4 (condensed_detachment) R->L }
% 44.92/6.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.04  = { by axiom 5 (cn_1) }
% 44.92/6.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.05  = { by axiom 1 (ifeq_axiom) }
% 44.92/6.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.05  = { by axiom 1 (ifeq_axiom) R->L }
% 44.92/6.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.05  = { by axiom 4 (condensed_detachment) R->L }
% 44.92/6.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.06  = { by axiom 5 (cn_1) }
% 44.92/6.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.06  = { by axiom 1 (ifeq_axiom) }
% 44.92/6.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.07  = { by axiom 1 (ifeq_axiom) R->L }
% 44.92/6.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.08  = { by axiom 5 (cn_1) R->L }
% 44.92/6.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.08  = { by axiom 1 (ifeq_axiom) R->L }
% 44.92/6.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.09  = { by axiom 4 (condensed_detachment) R->L }
% 44.92/6.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b)))), implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.10  = { by axiom 2 (cn_3) }
% 44.92/6.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b)))), implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.10  = { by axiom 1 (ifeq_axiom) }
% 44.92/6.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b)))), implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.11  = { by axiom 5 (cn_1) }
% 44.92/6.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 44.92/6.12  = { by axiom 1 (ifeq_axiom) }
% 45.63/6.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.12  = { by axiom 4 (condensed_detachment) }
% 45.63/6.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.13  = { by axiom 1 (ifeq_axiom) }
% 45.63/6.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.14  = { by axiom 1 (ifeq_axiom) R->L }
% 45.63/6.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true, ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.14  = { by axiom 4 (condensed_detachment) R->L }
% 45.63/6.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.15  = { by axiom 2 (cn_3) }
% 45.63/6.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.15  = { by axiom 1 (ifeq_axiom) }
% 45.63/6.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.15  = { by axiom 5 (cn_1) }
% 45.63/6.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.16  = { by axiom 1 (ifeq_axiom) }
% 45.63/6.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), not(implies(implies(not(b), a), implies(implies(a, b), b)))), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.16  = { by axiom 4 (condensed_detachment) }
% 45.63/6.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.16  = { by axiom 1 (ifeq_axiom) }
% 45.63/6.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(not(implies(implies(not(b), a), implies(implies(a, b), b)))), not(implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.16  = { by axiom 4 (condensed_detachment) }
% 45.63/6.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.17  = { by axiom 1 (ifeq_axiom) }
% 45.63/6.17    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.17  = { by axiom 1 (ifeq_axiom) R->L }
% 45.63/6.17    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.18  = { by axiom 4 (condensed_detachment) R->L }
% 45.63/6.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.18  = { by axiom 1 (ifeq_axiom) R->L }
% 45.63/6.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.19  = { by axiom 5 (cn_1) R->L }
% 45.63/6.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.19  = { by axiom 1 (ifeq_axiom) R->L }
% 45.63/6.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 45.63/6.20  = { by axiom 5 (cn_1) R->L }
% 46.17/6.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.20  = { by axiom 4 (condensed_detachment) }
% 46.17/6.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.21  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.21  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.22  = { by axiom 4 (condensed_detachment) R->L }
% 46.17/6.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.22  = { by axiom 3 (cn_2) }
% 46.17/6.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.23  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.23  = { by axiom 5 (cn_1) }
% 46.17/6.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.23  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.24  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.24  = { by axiom 5 (cn_1) R->L }
% 46.17/6.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.24  = { by axiom 4 (condensed_detachment) }
% 46.17/6.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.24  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.24    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(not(implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.24  = { by axiom 4 (condensed_detachment) }
% 46.17/6.24    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.24  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.24    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.25    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 4 (condensed_detachment) R->L }
% 46.17/6.25    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 5 (cn_1) }
% 46.17/6.25    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.25    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 5 (cn_1) }
% 46.17/6.25    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.25    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 4 (condensed_detachment) }
% 46.17/6.25    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.25    ifeq(ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.25    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 4 (condensed_detachment) R->L }
% 46.17/6.25    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.25    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 5 (cn_1) R->L }
% 46.17/6.25    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.25    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 5 (cn_1) R->L }
% 46.17/6.25    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(implies(a, b), b))), implies(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 4 (condensed_detachment) }
% 46.17/6.25    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.25  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.25    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.26  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.26    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.26  = { by axiom 4 (condensed_detachment) R->L }
% 46.17/6.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.26  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.26  = { by axiom 4 (condensed_detachment) R->L }
% 46.17/6.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true, ifeq(is_a_theorem(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b))), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.26  = { by axiom 3 (cn_2) }
% 46.17/6.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true, ifeq(true, true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.26  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.26  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.26  = { by axiom 4 (condensed_detachment) R->L }
% 46.17/6.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.26  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.27  = { by axiom 5 (cn_1) R->L }
% 46.17/6.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(implies(not(b), a)), implies(b, b))), implies(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.27  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(implies(not(b), a)), implies(b, b))), implies(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.27  = { by axiom 2 (cn_3) R->L }
% 46.17/6.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(implies(not(b), a)), implies(b, b))), implies(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))))), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(not(implies(not(b), a)), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.27  = { by axiom 4 (condensed_detachment) }
% 46.17/6.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.27  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.27  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.27  = { by axiom 4 (condensed_detachment) R->L }
% 46.17/6.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, b), implies(not(implies(b, b)), not(implies(not(b), a))))), true, ifeq(is_a_theorem(implies(b, b)), true, is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.27  = { by axiom 2 (cn_3) }
% 46.17/6.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(b, b)), true, is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.28  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(b, b)), true, is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.28  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.28  = { by axiom 4 (condensed_detachment) R->L }
% 46.17/6.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(b, b)))), true, ifeq(is_a_theorem(implies(b, implies(not(b), b))), true, is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true), true), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.28  = { by axiom 2 (cn_3) }
% 46.17/6.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(b, b)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true), true), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.28  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.28  = { by axiom 5 (cn_1) }
% 46.17/6.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.28  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.29  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true, ifeq(true, true, is_a_theorem(implies(b, b)), true), true), true, is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.29  = { by axiom 3 (cn_2) R->L }
% 46.17/6.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true, ifeq(is_a_theorem(implies(implies(not(b), b), b)), true, is_a_theorem(implies(b, b)), true), true), true, is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.29  = { by axiom 4 (condensed_detachment) }
% 46.17/6.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.29  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.29  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.29  = { by axiom 5 (cn_1) R->L }
% 46.17/6.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, b)), not(implies(not(b), a))), implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b))))), true, ifeq(is_a_theorem(implies(not(implies(b, b)), not(implies(not(b), a)))), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.29  = { by axiom 4 (condensed_detachment) }
% 46.17/6.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.29  = { by axiom 1 (ifeq_axiom) }
% 46.17/6.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.29  = { by axiom 1 (ifeq_axiom) R->L }
% 46.17/6.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.30  = { by axiom 5 (cn_1) R->L }
% 46.17/6.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b))), implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b))))), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(implies(not(b), a), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.17/6.30  = { by axiom 4 (condensed_detachment) }
% 46.88/6.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(b), a), implies(b, b))), true), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.30  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(b), a), implies(b, b))), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.30  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(b, b))), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.30  = { by axiom 5 (cn_1) R->L }
% 46.88/6.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(b, b)), implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b))))), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(b, b))), true, is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(not(b), a), implies(implies(not(b), b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.30  = { by axiom 4 (condensed_detachment) }
% 46.88/6.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.30  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.31  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.31  = { by axiom 5 (cn_1) R->L }
% 46.88/6.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(implies(b, b), implies(implies(not(b), b), b)))), true, is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.31  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(implies(b, b), implies(implies(not(b), b), b)))), true, ifeq(true, true, is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.31  = { by axiom 3 (cn_2) R->L }
% 46.88/6.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(implies(b, b), implies(implies(not(b), b), b)))), true, ifeq(is_a_theorem(implies(implies(not(b), b), b)), true, is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.31  = { by axiom 4 (condensed_detachment) }
% 46.88/6.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.31  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.31    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.31  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.31    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.31  = { by axiom 5 (cn_1) R->L }
% 46.88/6.31    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(not(b), b), b)), implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(implies(a, b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.31  = { by axiom 4 (condensed_detachment) }
% 46.88/6.31    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.31  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.31    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.31  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.31    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.31  = { by axiom 4 (condensed_detachment) R->L }
% 46.88/6.31    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), implies(not(b), b))), implies(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.31  = { by axiom 5 (cn_1) }
% 46.88/6.32    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.32  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.32    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.32  = { by axiom 5 (cn_1) }
% 46.88/6.32    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.32  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.32    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b))), implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(b), b)), implies(implies(not(b), a), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(not(b), a), implies(implies(not(b), a), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.32  = { by axiom 4 (condensed_detachment) }
% 46.88/6.32    ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.32  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.32    ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 46.88/6.32  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.32    ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.32  = { by axiom 4 (condensed_detachment) R->L }
% 46.88/6.32    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.32  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.32    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.32  = { by axiom 4 (condensed_detachment) R->L }
% 46.88/6.32    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(not(b), a)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(not(b), a))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.32  = { by axiom 3 (cn_2) }
% 46.88/6.32    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(not(b), a)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.32  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.32    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(not(b), a)), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.32  = { by axiom 5 (cn_1) }
% 46.88/6.33    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.33  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.33    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.33  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.33    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.33  = { by axiom 5 (cn_1) R->L }
% 46.88/6.33    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b))), implies(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))), implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.33  = { by axiom 4 (condensed_detachment) }
% 46.88/6.33    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.33  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.33    ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.33  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.33    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.33  = { by axiom 4 (condensed_detachment) R->L }
% 46.88/6.33    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.33  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.33    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.33  = { by axiom 4 (condensed_detachment) R->L }
% 46.88/6.33    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a))), implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a))))), true, ifeq(is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.34  = { by axiom 5 (cn_1) }
% 46.88/6.34    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.34  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.34    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.34  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.34    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.34  = { by axiom 4 (condensed_detachment) R->L }
% 46.88/6.34    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, a)), not(not(implies(not(b), a)))), implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))))), true, ifeq(is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.34  = { by axiom 5 (cn_1) }
% 46.88/6.34    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.35  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.35    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.35  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.35    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.35  = { by axiom 4 (condensed_detachment) R->L }
% 46.88/6.35    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true, ifeq(is_a_theorem(implies(implies(not(a), a), a)), true, is_a_theorem(implies(a, a)), true), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.35  = { by axiom 3 (cn_2) }
% 46.88/6.35    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.35  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.36    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.36  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.36    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.36  = { by axiom 5 (cn_1) R->L }
% 46.88/6.36    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.36  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.36    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(a, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.36  = { by axiom 2 (cn_3) R->L }
% 46.88/6.36    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(a, a)))), true, ifeq(is_a_theorem(implies(a, implies(not(a), a))), true, is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.37  = { by axiom 4 (condensed_detachment) }
% 46.88/6.37    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.37  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.37    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.37  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.37    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.38  = { by axiom 2 (cn_3) R->L }
% 46.88/6.38    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, a), implies(not(implies(a, a)), not(not(implies(not(b), a)))))), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(not(b), a))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.38  = { by axiom 4 (condensed_detachment) }
% 46.88/6.38    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.38  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.38    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.38  = { by axiom 1 (ifeq_axiom) R->L }
% 46.88/6.38    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.39  = { by axiom 4 (condensed_detachment) R->L }
% 46.88/6.39    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(not(not(implies(not(b), a))), implies(a, a))), implies(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))))), true, ifeq(is_a_theorem(implies(not(implies(not(b), a)), implies(not(not(implies(not(b), a))), implies(a, a)))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.39  = { by axiom 2 (cn_3) }
% 46.88/6.39    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(not(not(implies(not(b), a))), implies(a, a))), implies(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.39  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.39    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(not(not(implies(not(b), a))), implies(a, a))), implies(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.39  = { by axiom 5 (cn_1) }
% 46.88/6.39    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.39  = { by axiom 1 (ifeq_axiom) }
% 46.88/6.39    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(b), a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(not(b), a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 46.88/6.40  = { by axiom 4 (condensed_detachment) }
% 46.88/6.40    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.40  = { by axiom 1 (ifeq_axiom) }
% 47.58/6.40    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.40  = { by axiom 1 (ifeq_axiom) R->L }
% 47.58/6.40    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true, ifeq(true, true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.40  = { by axiom 3 (cn_2) R->L }
% 47.58/6.40    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(not(b), a)), implies(a, a)))), true, ifeq(is_a_theorem(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a))), true, is_a_theorem(implies(not(implies(not(b), a)), implies(a, a))), true), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.40  = { by axiom 4 (condensed_detachment) }
% 47.58/6.40    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.40  = { by axiom 1 (ifeq_axiom) }
% 47.58/6.40    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.40  = { by axiom 1 (ifeq_axiom) R->L }
% 47.58/6.40    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.40  = { by axiom 4 (condensed_detachment) R->L }
% 47.58/6.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(implies(a, a), implies(not(b), a))), implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))))), true, ifeq(is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.40  = { by axiom 5 (cn_1) }
% 47.58/6.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.41  = { by axiom 1 (ifeq_axiom) }
% 47.58/6.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.41  = { by axiom 1 (ifeq_axiom) R->L }
% 47.58/6.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.41  = { by axiom 4 (condensed_detachment) R->L }
% 47.58/6.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a))), implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.41  = { by axiom 1 (ifeq_axiom) R->L }
% 47.58/6.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a))), implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.41  = { by axiom 5 (cn_1) R->L }
% 47.58/6.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(not(b), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a))), implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.41  = { by axiom 1 (ifeq_axiom) R->L }
% 47.58/6.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(not(b), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a))), implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.42  = { by axiom 5 (cn_1) R->L }
% 47.58/6.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(not(b), a))), implies(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a))), implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))))), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(not(b), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a))), implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.42  = { by axiom 4 (condensed_detachment) }
% 47.58/6.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.42  = { by axiom 1 (ifeq_axiom) }
% 47.58/6.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.42  = { by axiom 1 (ifeq_axiom) R->L }
% 47.58/6.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.43  = { by axiom 4 (condensed_detachment) R->L }
% 47.58/6.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true, ifeq(is_a_theorem(implies(implies(not(a), a), a)), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.43  = { by axiom 3 (cn_2) }
% 47.58/6.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.43  = { by axiom 1 (ifeq_axiom) }
% 47.58/6.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.43  = { by axiom 5 (cn_1) }
% 47.58/6.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.43  = { by axiom 1 (ifeq_axiom) }
% 47.58/6.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.43  = { by axiom 1 (ifeq_axiom) R->L }
% 47.58/6.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.44  = { by axiom 5 (cn_1) R->L }
% 47.58/6.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), implies(implies(not(a), a), a)), implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a))))), true, ifeq(is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(not(b), a)), implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.44  = { by axiom 4 (condensed_detachment) }
% 47.58/6.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.44  = { by axiom 1 (ifeq_axiom) }
% 47.58/6.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.44  = { by axiom 1 (ifeq_axiom) R->L }
% 47.58/6.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.44  = { by axiom 4 (condensed_detachment) R->L }
% 47.58/6.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(b), implies(not(a), a))), implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a)))))), true, ifeq(is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.44  = { by axiom 5 (cn_1) }
% 47.58/6.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.45  = { by axiom 1 (ifeq_axiom) }
% 47.58/6.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.45  = { by axiom 1 (ifeq_axiom) R->L }
% 47.58/6.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.45  = { by axiom 4 (condensed_detachment) R->L }
% 47.58/6.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(implies(not(not(b)), a), implies(not(a), a))), implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a)))))), true, ifeq(is_a_theorem(implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.45  = { by axiom 5 (cn_1) }
% 47.58/6.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.46  = { by axiom 1 (ifeq_axiom) }
% 47.58/6.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.46  = { by axiom 1 (ifeq_axiom) R->L }
% 47.58/6.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.46  = { by axiom 5 (cn_1) R->L }
% 47.58/6.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a)))), true, is_a_theorem(implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.47  = { by axiom 1 (ifeq_axiom) R->L }
% 47.58/6.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a)))), true, is_a_theorem(implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.47  = { by axiom 4 (condensed_detachment) R->L }
% 47.58/6.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(a), not(not(b)))), implies(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a))), implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))))), true, ifeq(is_a_theorem(implies(a, implies(not(a), not(not(b))))), true, is_a_theorem(implies(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a))), implies(a, implies(implies(not(not(b)), a), implies(not(a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a)))), true, is_a_theorem(implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.48  = { by axiom 2 (cn_3) }
% 47.58/6.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(a), not(not(b)))), implies(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a))), implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a))), implies(a, implies(implies(not(not(b)), a), implies(not(a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a)))), true, is_a_theorem(implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.48  = { by axiom 1 (ifeq_axiom) }
% 47.58/6.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(a), not(not(b)))), implies(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a))), implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))))), true, is_a_theorem(implies(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a))), implies(a, implies(implies(not(not(b)), a), implies(not(a), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a)))), true, is_a_theorem(implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.48  = { by axiom 5 (cn_1) }
% 47.58/6.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a))), implies(a, implies(implies(not(not(b)), a), implies(not(a), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a)))), true, is_a_theorem(implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.48  = { by axiom 1 (ifeq_axiom) }
% 47.58/6.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a))), implies(a, implies(implies(not(not(b)), a), implies(not(a), a))))), true, ifeq(is_a_theorem(implies(implies(not(a), not(not(b))), implies(implies(not(not(b)), a), implies(not(a), a)))), true, is_a_theorem(implies(a, implies(implies(not(not(b)), a), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.49  = { by axiom 4 (condensed_detachment) }
% 47.58/6.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.49  = { by axiom 1 (ifeq_axiom) }
% 47.58/6.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.49  = { by axiom 1 (ifeq_axiom) R->L }
% 47.58/6.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 47.58/6.50  = { by axiom 4 (condensed_detachment) R->L }
% 48.30/6.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(b), implies(not(not(b)), a)), implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))))), true, ifeq(is_a_theorem(implies(not(b), implies(not(not(b)), a))), true, is_a_theorem(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a)))), true), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.50  = { by axiom 2 (cn_3) }
% 48.30/6.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(b), implies(not(not(b)), a)), implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a)))), true), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.50  = { by axiom 1 (ifeq_axiom) }
% 48.30/6.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(b), implies(not(not(b)), a)), implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))))), true, is_a_theorem(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.50  = { by axiom 5 (cn_1) }
% 48.30/6.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a)))), true), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.51  = { by axiom 1 (ifeq_axiom) }
% 48.30/6.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a))), implies(a, implies(not(b), implies(not(a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(b)), a), implies(not(a), a)), implies(not(b), implies(not(a), a)))), true, is_a_theorem(implies(a, implies(not(b), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.51  = { by axiom 4 (condensed_detachment) }
% 48.30/6.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.51  = { by axiom 1 (ifeq_axiom) }
% 48.30/6.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a))), implies(a, implies(implies(a, a), implies(not(b), a))))), true, ifeq(is_a_theorem(implies(implies(not(b), implies(not(a), a)), implies(implies(a, a), implies(not(b), a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.51  = { by axiom 4 (condensed_detachment) }
% 48.30/6.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.51  = { by axiom 1 (ifeq_axiom) }
% 48.30/6.51    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.51  = { by axiom 1 (ifeq_axiom) R->L }
% 48.30/6.52    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.52  = { by axiom 4 (condensed_detachment) R->L }
% 48.30/6.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a)))), implies(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.52  = { by axiom 5 (cn_1) }
% 48.30/6.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.52  = { by axiom 1 (ifeq_axiom) }
% 48.30/6.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.52  = { by axiom 5 (cn_1) }
% 48.30/6.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.52  = { by axiom 1 (ifeq_axiom) }
% 48.30/6.52    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(not(b), a)), implies(not(implies(not(b), a)), implies(not(b), a))), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true, is_a_theorem(implies(implies(not(implies(not(b), a)), implies(a, a)), implies(a, implies(not(implies(not(b), a)), implies(not(b), a))))), true), true), true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.52  = { by axiom 4 (condensed_detachment) }
% 48.30/6.52    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.52  = { by axiom 1 (ifeq_axiom) }
% 48.30/6.52    ifeq(ifeq(ifeq(is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.53  = { by axiom 1 (ifeq_axiom) R->L }
% 48.30/6.53    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.53  = { by axiom 5 (cn_1) R->L }
% 48.30/6.53    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(implies(not(b), a)), implies(not(b), a))), implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(a, implies(not(implies(not(b), a)), implies(not(b), a)))), true, is_a_theorem(implies(implies(implies(not(implies(not(b), a)), implies(not(b), a)), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.53  = { by axiom 4 (condensed_detachment) }
% 48.30/6.53    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.53  = { by axiom 1 (ifeq_axiom) }
% 48.30/6.53    ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(implies(a, b), b)), implies(a, implies(implies(a, b), b)))), true, ifeq(is_a_theorem(implies(implies(not(b), a), implies(implies(a, b), b))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 48.30/6.53  = { by axiom 4 (condensed_detachment) }
% 48.30/6.53    true
% 48.30/6.53  % SZS output end Proof
% 48.30/6.53  
% 48.30/6.53  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------