Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL053-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n017.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 11:48:55 AM UTC 2026

% Result   : Unsatisfiable 33.79s 4.71s
% Output   : Proof 52.90s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL053-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37  % Computer : n017.cluster.edu
% 0.09/0.37  % Model    : x86_64 x86_64
% 0.09/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37  % Memory   : 8046.5625MB
% 0.09/0.37  % OS       : Linux 6.8.0-71-generic
% 0.09/0.37  % CPULimit : 300
% 0.09/0.37  % WCLimit  : 300
% 0.09/0.37  % DateTime : Sun Sep 27 15:14:20 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.37  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.79/4.71  Command-line arguments: --no-flatten-goal
% 33.79/4.71  
% 33.79/4.71  % SZS status Unsatisfiable
% 33.79/4.71  
% 51.21/7.00  % SZS output start Proof
% 51.21/7.00  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 51.21/7.01  Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 51.21/7.01  Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 51.21/7.01  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.
% 52.41/7.07  Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 52.41/7.07  
% 52.41/7.07  Goal 1 (prove_cn_30): is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))) = true.
% 52.41/7.07  Proof:
% 52.41/7.07    is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b)))
% 52.41/7.07  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.07    ifeq(true, true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.07  = { by axiom 4 (condensed_detachment) R->L }
% 52.41/7.07    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.07  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.07    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.07  = { by axiom 4 (condensed_detachment) R->L }
% 52.41/7.07    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.07  = { by axiom 2 (cn_3) }
% 52.41/7.07    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.07  = { by axiom 1 (ifeq_axiom) }
% 52.41/7.07    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b))))), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.07  = { by axiom 5 (cn_1) }
% 52.41/7.07    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.07  = { by axiom 1 (ifeq_axiom) }
% 52.41/7.07    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.07  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.07    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.07  = { by axiom 3 (cn_2) R->L }
% 52.41/7.08    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(a, b)))), true, ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b))), true, is_a_theorem(implies(implies(a, b), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.08  = { by axiom 4 (condensed_detachment) }
% 52.41/7.08    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.08  = { by axiom 1 (ifeq_axiom) }
% 52.41/7.08    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.08  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.08    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.08  = { by axiom 4 (condensed_detachment) R->L }
% 52.41/7.08    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.08  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.08    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.08  = { by axiom 4 (condensed_detachment) R->L }
% 52.41/7.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(not(implies(a, b)), implies(implies(a, b), b))), implies(implies(implies(not(implies(a, b)), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(not(implies(a, b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.09  = { by axiom 5 (cn_1) }
% 52.41/7.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(not(implies(a, b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.09  = { by axiom 1 (ifeq_axiom) }
% 52.41/7.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(not(implies(a, b)), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.09  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(not(implies(a, b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.10  = { by axiom 5 (cn_1) R->L }
% 52.41/7.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(not(implies(a, b)), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(not(implies(a, b)), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.10  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(not(implies(a, b)), implies(implies(a, b), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(not(implies(a, b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.10  = { by axiom 2 (cn_3) R->L }
% 52.41/7.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(not(implies(a, b)), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(not(implies(a, b)), implies(not(not(implies(a, b))), not(implies(a, b))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(not(implies(a, b)), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.11  = { by axiom 4 (condensed_detachment) }
% 52.41/7.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.11  = { by axiom 1 (ifeq_axiom) }
% 52.41/7.11    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.11  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.11    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.11  = { by axiom 5 (cn_1) R->L }
% 52.41/7.11    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.11  = { by axiom 4 (condensed_detachment) }
% 52.41/7.11    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.12  = { by axiom 1 (ifeq_axiom) }
% 52.41/7.12    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.12  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.12    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.12  = { by axiom 4 (condensed_detachment) R->L }
% 52.41/7.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.12  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.13  = { by axiom 4 (condensed_detachment) R->L }
% 52.41/7.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.13  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.14  = { by axiom 5 (cn_1) R->L }
% 52.41/7.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.14  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.14  = { by axiom 2 (cn_3) R->L }
% 52.41/7.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.15  = { by axiom 4 (condensed_detachment) }
% 52.41/7.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.15  = { by axiom 1 (ifeq_axiom) }
% 52.41/7.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.15  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.16  = { by axiom 5 (cn_1) R->L }
% 52.41/7.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.16  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.16  = { by axiom 3 (cn_2) R->L }
% 52.41/7.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(a, b))), implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(a, b)))), true, is_a_theorem(implies(implies(not(implies(a, b)), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.17  = { by axiom 4 (condensed_detachment) }
% 52.41/7.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.17  = { by axiom 1 (ifeq_axiom) }
% 52.41/7.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.17  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.17  = { by axiom 5 (cn_1) R->L }
% 52.41/7.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.18  = { by axiom 4 (condensed_detachment) }
% 52.41/7.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.18  = { by axiom 1 (ifeq_axiom) }
% 52.41/7.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.41/7.18  = { by axiom 1 (ifeq_axiom) R->L }
% 52.41/7.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 46.94/7.19  = { by axiom 4 (condensed_detachment) R->L }
% 46.94/7.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 46.94/7.20  = { by axiom 1 (ifeq_axiom) R->L }
% 46.94/7.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 46.94/7.20  = { by axiom 4 (condensed_detachment) R->L }
% 46.94/7.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 46.94/7.21  = { by axiom 5 (cn_1) }
% 46.94/7.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 46.94/7.22  = { by axiom 1 (ifeq_axiom) }
% 46.94/7.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.25/7.23  = { by axiom 1 (ifeq_axiom) R->L }
% 47.25/7.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.25/7.24  = { by axiom 5 (cn_1) R->L }
% 47.25/7.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.25/7.24  = { by axiom 1 (ifeq_axiom) R->L }
% 47.25/7.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.25/7.25  = { by axiom 3 (cn_2) R->L }
% 47.25/7.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.25/7.26  = { by axiom 4 (condensed_detachment) }
% 47.25/7.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.25/7.27  = { by axiom 1 (ifeq_axiom) }
% 47.25/7.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.25/7.28  = { by axiom 1 (ifeq_axiom) R->L }
% 47.25/7.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.25/7.29  = { by axiom 4 (condensed_detachment) R->L }
% 47.73/7.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.73/7.30  = { by axiom 5 (cn_1) }
% 47.73/7.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.73/7.31  = { by axiom 1 (ifeq_axiom) }
% 47.73/7.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.73/7.32  = { by axiom 5 (cn_1) }
% 47.73/7.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.73/7.33  = { by axiom 1 (ifeq_axiom) }
% 47.73/7.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.73/7.33  = { by axiom 4 (condensed_detachment) }
% 47.73/7.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.73/7.34  = { by axiom 1 (ifeq_axiom) }
% 47.73/7.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.73/7.35  = { by axiom 1 (ifeq_axiom) R->L }
% 47.73/7.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.73/7.35  = { by axiom 4 (condensed_detachment) R->L }
% 47.73/7.35    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.73/7.36  = { by axiom 5 (cn_1) }
% 47.73/7.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.73/7.36  = { by axiom 1 (ifeq_axiom) }
% 47.73/7.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.73/7.37  = { by axiom 1 (ifeq_axiom) R->L }
% 47.73/7.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.73/7.38  = { by axiom 4 (condensed_detachment) R->L }
% 47.73/7.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 47.73/7.39  = { by axiom 1 (ifeq_axiom) R->L }
% 47.73/7.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 48.45/7.40  = { by axiom 5 (cn_1) R->L }
% 48.45/7.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 48.45/7.41  = { by axiom 1 (ifeq_axiom) R->L }
% 48.45/7.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 48.45/7.41  = { by axiom 5 (cn_1) R->L }
% 48.45/7.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 48.45/7.42  = { by axiom 4 (condensed_detachment) }
% 48.45/7.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 48.45/7.43  = { by axiom 1 (ifeq_axiom) }
% 48.45/7.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 48.45/7.44  = { by axiom 1 (ifeq_axiom) R->L }
% 48.45/7.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 48.45/7.45  = { by axiom 4 (condensed_detachment) R->L }
% 48.45/7.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 48.45/7.47  = { by axiom 1 (ifeq_axiom) R->L }
% 48.45/7.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 48.45/7.48  = { by axiom 5 (cn_1) R->L }
% 48.45/7.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b)))), implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 48.45/7.49  = { by axiom 1 (ifeq_axiom) R->L }
% 48.45/7.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b)))), implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 48.45/7.50  = { by axiom 2 (cn_3) R->L }
% 49.16/7.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b)))), implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.16/7.51  = { by axiom 4 (condensed_detachment) }
% 49.16/7.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.16/7.52  = { by axiom 1 (ifeq_axiom) }
% 49.16/7.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.16/7.53  = { by axiom 1 (ifeq_axiom) R->L }
% 49.16/7.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.16/7.54  = { by axiom 5 (cn_1) R->L }
% 49.16/7.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.16/7.54  = { by axiom 1 (ifeq_axiom) R->L }
% 49.16/7.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.16/7.55  = { by axiom 3 (cn_2) R->L }
% 49.16/7.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(a, b))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.16/7.56  = { by axiom 4 (condensed_detachment) }
% 49.16/7.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.16/7.57  = { by axiom 1 (ifeq_axiom) }
% 49.16/7.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.16/7.57  = { by axiom 1 (ifeq_axiom) R->L }
% 49.16/7.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.16/7.58  = { by axiom 5 (cn_1) R->L }
% 49.16/7.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b)))), implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(implies(a, b))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.16/7.59  = { by axiom 4 (condensed_detachment) }
% 49.16/7.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.16/7.59  = { by axiom 1 (ifeq_axiom) }
% 49.16/7.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.87/7.60  = { by axiom 1 (ifeq_axiom) R->L }
% 49.87/7.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.87/7.61  = { by axiom 4 (condensed_detachment) R->L }
% 49.87/7.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.87/7.62  = { by axiom 5 (cn_1) }
% 49.87/7.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.87/7.63  = { by axiom 1 (ifeq_axiom) }
% 49.87/7.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.87/7.64  = { by axiom 1 (ifeq_axiom) R->L }
% 49.87/7.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.87/7.65  = { by axiom 4 (condensed_detachment) R->L }
% 49.87/7.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.87/7.66  = { by axiom 5 (cn_1) }
% 49.87/7.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.87/7.67  = { by axiom 1 (ifeq_axiom) }
% 49.87/7.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 49.87/7.69  = { by axiom 1 (ifeq_axiom) R->L }
% 49.87/7.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 50.58/7.71  = { by axiom 5 (cn_1) R->L }
% 50.58/7.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 50.58/7.73  = { by axiom 1 (ifeq_axiom) R->L }
% 50.58/7.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 50.58/7.75  = { by axiom 4 (condensed_detachment) R->L }
% 50.58/7.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b)))))), implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 50.58/7.76  = { by axiom 2 (cn_3) }
% 50.58/7.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b)))))), implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 50.58/7.78  = { by axiom 1 (ifeq_axiom) }
% 50.58/7.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b)))))), implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 50.58/7.79  = { by axiom 5 (cn_1) }
% 51.27/7.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.27/7.81  = { by axiom 1 (ifeq_axiom) }
% 51.27/7.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.27/7.82  = { by axiom 4 (condensed_detachment) }
% 51.27/7.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.27/7.84  = { by axiom 1 (ifeq_axiom) }
% 51.27/7.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.27/7.85  = { by axiom 1 (ifeq_axiom) R->L }
% 51.27/7.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true, ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.27/7.87  = { by axiom 4 (condensed_detachment) R->L }
% 51.27/7.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.27/7.88  = { by axiom 2 (cn_3) }
% 51.27/7.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.27/7.89  = { by axiom 1 (ifeq_axiom) }
% 51.98/7.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.90  = { by axiom 5 (cn_1) }
% 51.98/7.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.91  = { by axiom 1 (ifeq_axiom) }
% 51.98/7.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(a, b)))), not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.92  = { by axiom 4 (condensed_detachment) }
% 51.98/7.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.92  = { by axiom 1 (ifeq_axiom) }
% 51.98/7.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(not(not(not(implies(not(not(implies(a, b))), not(implies(a, b)))))), not(not(implies(not(not(implies(a, b))), not(implies(a, b))))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.93  = { by axiom 4 (condensed_detachment) }
% 51.98/7.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.93  = { by axiom 1 (ifeq_axiom) }
% 51.98/7.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.94  = { by axiom 1 (ifeq_axiom) R->L }
% 51.98/7.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.95  = { by axiom 4 (condensed_detachment) R->L }
% 51.98/7.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.95  = { by axiom 5 (cn_1) }
% 51.98/7.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.96  = { by axiom 1 (ifeq_axiom) }
% 51.98/7.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.97  = { by axiom 1 (ifeq_axiom) R->L }
% 51.98/7.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.98  = { by axiom 5 (cn_1) R->L }
% 51.98/7.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.98  = { by axiom 1 (ifeq_axiom) R->L }
% 51.98/7.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.99  = { by axiom 3 (cn_2) R->L }
% 51.98/7.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/7.99  = { by axiom 4 (condensed_detachment) }
% 51.98/8.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/8.00  = { by axiom 1 (ifeq_axiom) }
% 51.98/8.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/8.00  = { by axiom 4 (condensed_detachment) }
% 51.98/8.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/8.01  = { by axiom 1 (ifeq_axiom) }
% 51.98/8.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/8.01  = { by axiom 1 (ifeq_axiom) R->L }
% 51.98/8.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/8.01  = { by axiom 4 (condensed_detachment) R->L }
% 51.98/8.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/8.02  = { by axiom 3 (cn_2) }
% 51.98/8.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(true, true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/8.02  = { by axiom 1 (ifeq_axiom) }
% 51.98/8.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 51.98/8.03  = { by axiom 1 (ifeq_axiom) R->L }
% 51.98/8.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.03  = { by axiom 5 (cn_1) R->L }
% 52.90/8.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.03  = { by axiom 1 (ifeq_axiom) R->L }
% 52.90/8.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.04  = { by axiom 2 (cn_3) R->L }
% 52.90/8.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.04  = { by axiom 4 (condensed_detachment) }
% 52.90/8.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.04  = { by axiom 1 (ifeq_axiom) }
% 52.90/8.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), not(implies(not(not(implies(a, b))), not(implies(a, b))))), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.05  = { by axiom 4 (condensed_detachment) }
% 52.90/8.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.05  = { by axiom 1 (ifeq_axiom) }
% 52.90/8.05    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.05  = { by axiom 1 (ifeq_axiom) R->L }
% 52.90/8.05    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.06  = { by axiom 4 (condensed_detachment) R->L }
% 52.90/8.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.06  = { by axiom 1 (ifeq_axiom) R->L }
% 52.90/8.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.06  = { by axiom 5 (cn_1) R->L }
% 52.90/8.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b)), implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.07  = { by axiom 1 (ifeq_axiom) R->L }
% 52.90/8.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b)), implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.07  = { by axiom 2 (cn_3) R->L }
% 52.90/8.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b)), implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.07  = { by axiom 4 (condensed_detachment) }
% 52.90/8.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.08  = { by axiom 1 (ifeq_axiom) }
% 52.90/8.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.08  = { by axiom 1 (ifeq_axiom) R->L }
% 52.90/8.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.08  = { by axiom 5 (cn_1) R->L }
% 52.90/8.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.08  = { by axiom 1 (ifeq_axiom) R->L }
% 52.90/8.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.08  = { by axiom 5 (cn_1) R->L }
% 52.90/8.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b))), implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(a, b))), not(implies(a, b)))), b), implies(implies(a, b), b)), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.09  = { by axiom 4 (condensed_detachment) }
% 52.90/8.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.09  = { by axiom 1 (ifeq_axiom) }
% 52.90/8.09    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b))))), implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b)))), true, ifeq(is_a_theorem(implies(implies(a, b), not(implies(not(not(implies(a, b))), not(implies(a, b)))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(a, b))), implies(implies(a, b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.09  = { by axiom 4 (condensed_detachment) }
% 52.90/8.09    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.09  = { by axiom 1 (ifeq_axiom) }
% 52.90/8.09    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.09  = { by axiom 1 (ifeq_axiom) R->L }
% 52.90/8.09    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.09  = { by axiom 4 (condensed_detachment) R->L }
% 52.90/8.09    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.10  = { by axiom 1 (ifeq_axiom) R->L }
% 52.90/8.10    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.10  = { by axiom 5 (cn_1) R->L }
% 52.90/8.10    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.10  = { by axiom 1 (ifeq_axiom) R->L }
% 52.90/8.10    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.10  = { by axiom 5 (cn_1) R->L }
% 52.90/8.10    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.11  = { by axiom 4 (condensed_detachment) }
% 52.90/8.11    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.11  = { by axiom 1 (ifeq_axiom) }
% 52.90/8.11    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.11  = { by axiom 1 (ifeq_axiom) R->L }
% 52.90/8.11    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.11  = { by axiom 4 (condensed_detachment) R->L }
% 52.90/8.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.11  = { by axiom 3 (cn_2) }
% 52.90/8.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.11  = { by axiom 1 (ifeq_axiom) }
% 52.90/8.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(a, b)), implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.12  = { by axiom 5 (cn_1) }
% 52.90/8.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.12  = { by axiom 1 (ifeq_axiom) }
% 52.90/8.12    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.12  = { by axiom 1 (ifeq_axiom) R->L }
% 52.90/8.12    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.12  = { by axiom 5 (cn_1) R->L }
% 52.90/8.12    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, b)), implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b))), implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.12  = { by axiom 4 (condensed_detachment) }
% 52.90/8.12    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.12  = { by axiom 1 (ifeq_axiom) }
% 52.90/8.12    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, b)), implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.12  = { by axiom 4 (condensed_detachment) }
% 52.90/8.12    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.12  = { by axiom 1 (ifeq_axiom) }
% 52.90/8.12    ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true)
% 52.90/8.12  = { by axiom 1 (ifeq_axiom) R->L }
% 52.90/8.12    ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true), true)
% 52.90/8.12  = { by axiom 4 (condensed_detachment) R->L }
% 52.90/8.12    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(a, b)), implies(implies(implies(a, b), b), implies(a, b))), implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)), implies(implies(a, implies(a, b)), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(a, implies(a, b)), implies(implies(implies(a, b), b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)), implies(implies(a, implies(a, b)), implies(a, b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true), true)
% 52.90/8.12  = { by axiom 5 (cn_1) }
% 52.90/8.12    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(a, b)), implies(implies(implies(a, b), b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)), implies(implies(a, implies(a, b)), implies(a, b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true), true)
% 52.90/8.12  = { by axiom 1 (ifeq_axiom) }
% 52.90/8.12    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, b)), implies(implies(implies(a, b), b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)), implies(implies(a, implies(a, b)), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true), true)
% 52.90/8.12  = { by axiom 5 (cn_1) }
% 52.90/8.12    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)), implies(implies(a, implies(a, b)), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true), true)
% 52.90/8.12  = { by axiom 1 (ifeq_axiom) }
% 52.90/8.13    ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b)), implies(implies(a, implies(a, b)), implies(a, b)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), implies(a, b)), implies(a, b))), true, is_a_theorem(implies(implies(a, implies(a, b)), implies(a, b))), true), true)
% 52.90/8.13  = { by axiom 4 (condensed_detachment) }
% 52.90/8.13    true
% 52.90/8.13  % SZS output end Proof
% 52.90/8.13  
% 52.90/8.13  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------